Deck 7: Integration Techniques

ملء الشاشة (f)
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سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
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لقلب البطاقة.
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.    </strong> A)     B)   C)   D)   <div style=padding-top: 35px> <strong>Evaluate the integral.    </strong> A)     B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.    </strong> A)     B)   C)   D)   <div style=padding-top: 35px> <strong>Evaluate the integral.    </strong> A)     B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.    </strong> A)     B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.    </strong> A)     B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.    </strong> A)     B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.    </strong> A)   B)   C)   D)   <div style=padding-top: 35px> <strong>Evaluate the integral.    </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.    </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.    </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.    </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.    </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot). <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).   and  </strong> A)   B)   C)   D)   <div style=padding-top: 35px> and <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).   and  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).   and  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).   and  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).   and  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).   and  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot). <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.    </strong> A)   B)   C)   D)   <div style=padding-top: 35px> <strong>Evaluate the integral.    </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.    </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.    </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.    </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.    </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find <strong>Find   where  </strong> A)   B)   C)   D)   <div style=padding-top: 35px> where <strong>Find   where  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find   where  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find   where  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find   where  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find   where  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find <strong>Find  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot). <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).     and  </strong> A)   B)   C)   D)   <div style=padding-top: 35px> <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).     and  </strong> A)   B)   C)   D)   <div style=padding-top: 35px> and <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).     and  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).     and  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).     and  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).     and  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).     and  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. (Hint: you may need to use a reduction formula.) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral using integration by parts and substitution. <strong>Evaluate the integral using integration by parts and substitution.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral using integration by parts and substitution.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral using integration by parts and substitution.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral using integration by parts and substitution.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral using integration by parts and substitution.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral using integration by parts and substitution (as we recommended in the text, "Try something!"). <strong>Evaluate the integral using integration by parts and substitution (as we recommended in the text, Try something!).  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral using integration by parts and substitution (as we recommended in the text, Try something!).  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral using integration by parts and substitution (as we recommended in the text, Try something!).  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral using integration by parts and substitution (as we recommended in the text, Try something!).  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral using integration by parts and substitution (as we recommended in the text, Try something!).  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. Evaluate the integral.  <div style=padding-top: 35px>
سؤال
Several useful integration formulas called reduction formulas are used to automate the process of performing multiple integrations by parts. Prove that for any positive integer Several useful integration formulas called reduction formulas are used to automate the process of performing multiple integrations by parts. Prove that for any positive integer   ,   (Use integration by parts with   ).<div style=padding-top: 35px> , Several useful integration formulas called reduction formulas are used to automate the process of performing multiple integrations by parts. Prove that for any positive integer   ,   (Use integration by parts with   ).<div style=padding-top: 35px> (Use integration by parts with Several useful integration formulas called reduction formulas are used to automate the process of performing multiple integrations by parts. Prove that for any positive integer   ,   (Use integration by parts with   ).<div style=padding-top: 35px> ).
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. (Hint: you may need to use a reduction formula.) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral using integration by parts and substitution (as we recommended in the text, "Try something!"). <strong>Evaluate the integral using integration by parts and substitution (as we recommended in the text, Try something!).  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral using integration by parts and substitution (as we recommended in the text, Try something!).  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral using integration by parts and substitution (as we recommended in the text, Try something!).  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral using integration by parts and substitution (as we recommended in the text, Try something!).  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral using integration by parts and substitution (as we recommended in the text, Try something!).  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. (Hint: you may need to use a reduction formula.) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find an antiderivative. <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find the partial fraction decomposition. <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find an antiderivative. <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
In an AC circuit, the current has the form <strong>In an AC circuit, the current has the form   for constants   The power is defined as   for a constant   . Find the average value of the power by integrating over the interval  </strong> A)   B)   C)   D)   <div style=padding-top: 35px> for constants <strong>In an AC circuit, the current has the form   for constants   The power is defined as   for a constant   . Find the average value of the power by integrating over the interval  </strong> A)   B)   C)   D)   <div style=padding-top: 35px> The power is defined as <strong>In an AC circuit, the current has the form   for constants   The power is defined as   for a constant   . Find the average value of the power by integrating over the interval  </strong> A)   B)   C)   D)   <div style=padding-top: 35px> for a constant <strong>In an AC circuit, the current has the form   for constants   The power is defined as   for a constant   . Find the average value of the power by integrating over the interval  </strong> A)   B)   C)   D)   <div style=padding-top: 35px> . Find the average value of the power by integrating over the interval <strong>In an AC circuit, the current has the form   for constants   The power is defined as   for a constant   . Find the average value of the power by integrating over the interval  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>In an AC circuit, the current has the form   for constants   The power is defined as   for a constant   . Find the average value of the power by integrating over the interval  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>In an AC circuit, the current has the form   for constants   The power is defined as   for a constant   . Find the average value of the power by integrating over the interval  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>In an AC circuit, the current has the form   for constants   The power is defined as   for a constant   . Find the average value of the power by integrating over the interval  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>In an AC circuit, the current has the form   for constants   The power is defined as   for a constant   . Find the average value of the power by integrating over the interval  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find an antiderivative. <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find the partial fraction decomposition. <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. Evaluate the integral.  <div style=padding-top: 35px>
سؤال
Find the partial fraction decomposition. <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find an antiderivative. <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find the partial fraction decomposition. <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find the partial fraction decomposition. <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find an antiderivative. <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find an antiderivative. <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find the partial fraction decomposition. <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Use a table of integrals to find an antiderivative. <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find the partial fraction decomposition. <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find the partial fraction decomposition. <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find the partial fraction decomposition. <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Determine whether or not the integral is improper. <strong>Determine whether or not the integral is improper.  </strong> A) The integral is improper. B) The integral is not improper. <div style=padding-top: 35px>

A) The integral is improper.
B) The integral is not improper.
سؤال
Find the partial fractions decomposition and an antiderivative. Find the partial fractions decomposition and an antiderivative.  <div style=padding-top: 35px>
سؤال
Use a table of integrals to find an antiderivative. <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Determine whether the integral converges or diverges. Find the value of the integral if it converges. <strong>Determine whether the integral converges or diverges. Find the value of the integral if it converges.  </strong> A) The integral diverges. B) The integral evaluates to   . C) The integral evaluates to   . D) The integral evaluates to   . <div style=padding-top: 35px>

A) The integral diverges.
B) The integral evaluates to <strong>Determine whether the integral converges or diverges. Find the value of the integral if it converges.  </strong> A) The integral diverges. B) The integral evaluates to   . C) The integral evaluates to   . D) The integral evaluates to   . <div style=padding-top: 35px> .
C) The integral evaluates to <strong>Determine whether the integral converges or diverges. Find the value of the integral if it converges.  </strong> A) The integral diverges. B) The integral evaluates to   . C) The integral evaluates to   . D) The integral evaluates to   . <div style=padding-top: 35px> .
D) The integral evaluates to <strong>Determine whether the integral converges or diverges. Find the value of the integral if it converges.  </strong> A) The integral diverges. B) The integral evaluates to   . C) The integral evaluates to   . D) The integral evaluates to   . <div style=padding-top: 35px> .
سؤال
Determine whether the integral converges or diverges. Find the value of the integral if it converges. <strong>Determine whether the integral converges or diverges. Find the value of the integral if it converges.  </strong> A) The integral diverges. B) The integral evaluates to   . C) The integral evaluates to   . D) The integral evaluates to   . <div style=padding-top: 35px>

A) The integral diverges.
B) The integral evaluates to <strong>Determine whether the integral converges or diverges. Find the value of the integral if it converges.  </strong> A) The integral diverges. B) The integral evaluates to   . C) The integral evaluates to   . D) The integral evaluates to   . <div style=padding-top: 35px> .
C) The integral evaluates to <strong>Determine whether the integral converges or diverges. Find the value of the integral if it converges.  </strong> A) The integral diverges. B) The integral evaluates to   . C) The integral evaluates to   . D) The integral evaluates to   . <div style=padding-top: 35px> .
D) The integral evaluates to <strong>Determine whether the integral converges or diverges. Find the value of the integral if it converges.  </strong> A) The integral diverges. B) The integral evaluates to   . C) The integral evaluates to   . D) The integral evaluates to   . <div style=padding-top: 35px> .
سؤال
Use a table of integrals to evaluate the definite integral. <strong>Use a table of integrals to evaluate the definite integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Use a table of integrals to evaluate the definite integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Use a table of integrals to evaluate the definite integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Use a table of integrals to evaluate the definite integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Use a table of integrals to evaluate the definite integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Determine whether or not the integral is improper. <strong>Determine whether or not the integral is improper.  </strong> A) The integral is improper. B) The integral is not improper. <div style=padding-top: 35px>

A) The integral is improper.
B) The integral is not improper.
سؤال
Use a table of integrals to find an antiderivative. <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Use a table of integrals to find an antiderivative. <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Use an integral formula to evaluate the integral. <strong>Use an integral formula to evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Use an integral formula to evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Use an integral formula to evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Use an integral formula to evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Use an integral formula to evaluate the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Use a table of integrals to find an antiderivative. <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Use a table of integrals to find an antiderivative. <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Use a table of integrals to find an antiderivative. <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Determine whether or not the integral is improper. <strong>Determine whether or not the integral is improper.  </strong> A) The integral is improper. B) The integral is not improper. <div style=padding-top: 35px>

A) The integral is improper.
B) The integral is not improper.
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Deck 7: Integration Techniques
1
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C
2
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
A
3
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
A
4
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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5
Evaluate the integral. <strong>Evaluate the integral.    </strong> A)     B)   C)   D)   <strong>Evaluate the integral.    </strong> A)     B)   C)   D)

A) <strong>Evaluate the integral.    </strong> A)     B)   C)   D)   <strong>Evaluate the integral.    </strong> A)     B)   C)   D)
B) <strong>Evaluate the integral.    </strong> A)     B)   C)   D)
C) <strong>Evaluate the integral.    </strong> A)     B)   C)   D)
D) <strong>Evaluate the integral.    </strong> A)     B)   C)   D)
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6
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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7
Evaluate the integral. <strong>Evaluate the integral.    </strong> A)   B)   C)   D)   <strong>Evaluate the integral.    </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.    </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.    </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.    </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.    </strong> A)   B)   C)   D)
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8
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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9
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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10
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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11
You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot). <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).   and  </strong> A)   B)   C)   D)   and <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).   and  </strong> A)   B)   C)   D)

A) <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).   and  </strong> A)   B)   C)   D)
B) <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).   and  </strong> A)   B)   C)   D)
C) <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).   and  </strong> A)   B)   C)   D)
D) <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).   and  </strong> A)   B)   C)   D)
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12
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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13
You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot). <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).  </strong> A)   B)   C)   D)

A) <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).  </strong> A)   B)   C)   D)
B) <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).  </strong> A)   B)   C)   D)
C) <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).  </strong> A)   B)   C)   D)
D) <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).  </strong> A)   B)   C)   D)
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14
Evaluate the integral. <strong>Evaluate the integral.    </strong> A)   B)   C)   D)   <strong>Evaluate the integral.    </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.    </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.    </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.    </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.    </strong> A)   B)   C)   D)
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15
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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16
Find <strong>Find   where  </strong> A)   B)   C)   D)   where <strong>Find   where  </strong> A)   B)   C)   D)

A) <strong>Find   where  </strong> A)   B)   C)   D)
B) <strong>Find   where  </strong> A)   B)   C)   D)
C) <strong>Find   where  </strong> A)   B)   C)   D)
D) <strong>Find   where  </strong> A)   B)   C)   D)
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17
Find <strong>Find  </strong> A)   B)   C)   D)

A) <strong>Find  </strong> A)   B)   C)   D)
B) <strong>Find  </strong> A)   B)   C)   D)
C) <strong>Find  </strong> A)   B)   C)   D)
D) <strong>Find  </strong> A)   B)   C)   D)
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18
You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot). <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).     and  </strong> A)   B)   C)   D)   <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).     and  </strong> A)   B)   C)   D)   and <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).     and  </strong> A)   B)   C)   D)

A) <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).     and  </strong> A)   B)   C)   D)
B) <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).     and  </strong> A)   B)   C)   D)
C) <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).     and  </strong> A)   B)   C)   D)
D) <strong>You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).     and  </strong> A)   B)   C)   D)
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19
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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20
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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21
Evaluate the integral. (Hint: you may need to use a reduction formula.) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)
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22
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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23
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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24
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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25
Evaluate the integral using integration by parts and substitution. <strong>Evaluate the integral using integration by parts and substitution.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral using integration by parts and substitution.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral using integration by parts and substitution.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral using integration by parts and substitution.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral using integration by parts and substitution.  </strong> A)   B)   C)   D)
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26
Evaluate the integral using integration by parts and substitution (as we recommended in the text, "Try something!"). <strong>Evaluate the integral using integration by parts and substitution (as we recommended in the text, Try something!).  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral using integration by parts and substitution (as we recommended in the text, Try something!).  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral using integration by parts and substitution (as we recommended in the text, Try something!).  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral using integration by parts and substitution (as we recommended in the text, Try something!).  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral using integration by parts and substitution (as we recommended in the text, Try something!).  </strong> A)   B)   C)   D)
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27
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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28
Evaluate the integral. Evaluate the integral.
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29
Several useful integration formulas called reduction formulas are used to automate the process of performing multiple integrations by parts. Prove that for any positive integer Several useful integration formulas called reduction formulas are used to automate the process of performing multiple integrations by parts. Prove that for any positive integer   ,   (Use integration by parts with   ). , Several useful integration formulas called reduction formulas are used to automate the process of performing multiple integrations by parts. Prove that for any positive integer   ,   (Use integration by parts with   ). (Use integration by parts with Several useful integration formulas called reduction formulas are used to automate the process of performing multiple integrations by parts. Prove that for any positive integer   ,   (Use integration by parts with   ). ).
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30
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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31
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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32
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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33
Evaluate the integral. (Hint: you may need to use a reduction formula.) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)
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34
Evaluate the integral using integration by parts and substitution (as we recommended in the text, "Try something!"). <strong>Evaluate the integral using integration by parts and substitution (as we recommended in the text, Try something!).  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral using integration by parts and substitution (as we recommended in the text, Try something!).  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral using integration by parts and substitution (as we recommended in the text, Try something!).  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral using integration by parts and substitution (as we recommended in the text, Try something!).  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral using integration by parts and substitution (as we recommended in the text, Try something!).  </strong> A)   B)   C)   D)
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35
Evaluate the integral. (Hint: you may need to use a reduction formula.) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral. (Hint: you may need to use a reduction formula.)  </strong> A)   B)   C)   D)
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36
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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37
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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38
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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39
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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40
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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41
Find an antiderivative. <strong>Find an antiderivative.  </strong> A)   B)   C)   D)

A) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)
B) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)
C) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)
D) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)
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42
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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43
Find the partial fraction decomposition. <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)

A) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
B) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
C) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
D) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
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44
Find an antiderivative. <strong>Find an antiderivative.  </strong> A)   B)   C)   D)

A) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)
B) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)
C) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)
D) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)
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45
In an AC circuit, the current has the form <strong>In an AC circuit, the current has the form   for constants   The power is defined as   for a constant   . Find the average value of the power by integrating over the interval  </strong> A)   B)   C)   D)   for constants <strong>In an AC circuit, the current has the form   for constants   The power is defined as   for a constant   . Find the average value of the power by integrating over the interval  </strong> A)   B)   C)   D)   The power is defined as <strong>In an AC circuit, the current has the form   for constants   The power is defined as   for a constant   . Find the average value of the power by integrating over the interval  </strong> A)   B)   C)   D)   for a constant <strong>In an AC circuit, the current has the form   for constants   The power is defined as   for a constant   . Find the average value of the power by integrating over the interval  </strong> A)   B)   C)   D)   . Find the average value of the power by integrating over the interval <strong>In an AC circuit, the current has the form   for constants   The power is defined as   for a constant   . Find the average value of the power by integrating over the interval  </strong> A)   B)   C)   D)

A) <strong>In an AC circuit, the current has the form   for constants   The power is defined as   for a constant   . Find the average value of the power by integrating over the interval  </strong> A)   B)   C)   D)
B) <strong>In an AC circuit, the current has the form   for constants   The power is defined as   for a constant   . Find the average value of the power by integrating over the interval  </strong> A)   B)   C)   D)
C) <strong>In an AC circuit, the current has the form   for constants   The power is defined as   for a constant   . Find the average value of the power by integrating over the interval  </strong> A)   B)   C)   D)
D) <strong>In an AC circuit, the current has the form   for constants   The power is defined as   for a constant   . Find the average value of the power by integrating over the interval  </strong> A)   B)   C)   D)
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46
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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47
Find an antiderivative. <strong>Find an antiderivative.  </strong> A)   B)   C)   D)

A) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)
B) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)
C) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)
D) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)
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48
Find the partial fraction decomposition. <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)

A) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
B) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
C) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
D) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
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49
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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50
Evaluate the integral. Evaluate the integral.
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51
Find the partial fraction decomposition. <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)

A) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
B) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
C) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
D) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
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52
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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53
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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54
Find an antiderivative. <strong>Find an antiderivative.  </strong> A)   B)   C)   D)

A) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)
B) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)
C) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)
D) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)
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55
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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56
Find the partial fraction decomposition. <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)

A) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
B) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
C) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
D) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
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57
Find the partial fraction decomposition. <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)

A) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
B) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
C) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
D) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
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58
Find an antiderivative. <strong>Find an antiderivative.  </strong> A)   B)   C)   D)

A) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)
B) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)
C) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)
D) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)
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59
Find an antiderivative. <strong>Find an antiderivative.  </strong> A)   B)   C)   D)

A) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)
B) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)
C) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)
D) <strong>Find an antiderivative.  </strong> A)   B)   C)   D)
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60
Find the partial fraction decomposition. <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)

A) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
B) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
C) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
D) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
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61
Use a table of integrals to find an antiderivative. <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)

A) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
B) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
C) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
D) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
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62
Find the partial fraction decomposition. <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)

A) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
B) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
C) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
D) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
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63
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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64
Find the partial fraction decomposition. <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)

A) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
B) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
C) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
D) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
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65
Find the partial fraction decomposition. <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)

A) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
B) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
C) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
D) <strong>Find the partial fraction decomposition.  </strong> A)   B)   C)   D)
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66
Determine whether or not the integral is improper. <strong>Determine whether or not the integral is improper.  </strong> A) The integral is improper. B) The integral is not improper.

A) The integral is improper.
B) The integral is not improper.
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67
Find the partial fractions decomposition and an antiderivative. Find the partial fractions decomposition and an antiderivative.
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68
Use a table of integrals to find an antiderivative. <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)

A) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
B) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
C) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
D) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
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69
Determine whether the integral converges or diverges. Find the value of the integral if it converges. <strong>Determine whether the integral converges or diverges. Find the value of the integral if it converges.  </strong> A) The integral diverges. B) The integral evaluates to   . C) The integral evaluates to   . D) The integral evaluates to   .

A) The integral diverges.
B) The integral evaluates to <strong>Determine whether the integral converges or diverges. Find the value of the integral if it converges.  </strong> A) The integral diverges. B) The integral evaluates to   . C) The integral evaluates to   . D) The integral evaluates to   . .
C) The integral evaluates to <strong>Determine whether the integral converges or diverges. Find the value of the integral if it converges.  </strong> A) The integral diverges. B) The integral evaluates to   . C) The integral evaluates to   . D) The integral evaluates to   . .
D) The integral evaluates to <strong>Determine whether the integral converges or diverges. Find the value of the integral if it converges.  </strong> A) The integral diverges. B) The integral evaluates to   . C) The integral evaluates to   . D) The integral evaluates to   . .
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70
Determine whether the integral converges or diverges. Find the value of the integral if it converges. <strong>Determine whether the integral converges or diverges. Find the value of the integral if it converges.  </strong> A) The integral diverges. B) The integral evaluates to   . C) The integral evaluates to   . D) The integral evaluates to   .

A) The integral diverges.
B) The integral evaluates to <strong>Determine whether the integral converges or diverges. Find the value of the integral if it converges.  </strong> A) The integral diverges. B) The integral evaluates to   . C) The integral evaluates to   . D) The integral evaluates to   . .
C) The integral evaluates to <strong>Determine whether the integral converges or diverges. Find the value of the integral if it converges.  </strong> A) The integral diverges. B) The integral evaluates to   . C) The integral evaluates to   . D) The integral evaluates to   . .
D) The integral evaluates to <strong>Determine whether the integral converges or diverges. Find the value of the integral if it converges.  </strong> A) The integral diverges. B) The integral evaluates to   . C) The integral evaluates to   . D) The integral evaluates to   . .
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71
Use a table of integrals to evaluate the definite integral. <strong>Use a table of integrals to evaluate the definite integral.  </strong> A)   B)   C)   D)

A) <strong>Use a table of integrals to evaluate the definite integral.  </strong> A)   B)   C)   D)
B) <strong>Use a table of integrals to evaluate the definite integral.  </strong> A)   B)   C)   D)
C) <strong>Use a table of integrals to evaluate the definite integral.  </strong> A)   B)   C)   D)
D) <strong>Use a table of integrals to evaluate the definite integral.  </strong> A)   B)   C)   D)
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72
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)
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73
Determine whether or not the integral is improper. <strong>Determine whether or not the integral is improper.  </strong> A) The integral is improper. B) The integral is not improper.

A) The integral is improper.
B) The integral is not improper.
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74
Use a table of integrals to find an antiderivative. <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)

A) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
B) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
C) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
D) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
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75
Use a table of integrals to find an antiderivative. <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)

A) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
B) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
C) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
D) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
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76
Use an integral formula to evaluate the integral. <strong>Use an integral formula to evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Use an integral formula to evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Use an integral formula to evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Use an integral formula to evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Use an integral formula to evaluate the integral.  </strong> A)   B)   C)   D)
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77
Use a table of integrals to find an antiderivative. <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)

A) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
B) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
C) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
D) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
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78
Use a table of integrals to find an antiderivative. <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)

A) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
B) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
C) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
D) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
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79
Use a table of integrals to find an antiderivative. <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)

A) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
B) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
C) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
D) <strong>Use a table of integrals to find an antiderivative.  </strong> A)   B)   C)   D)
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80
Determine whether or not the integral is improper. <strong>Determine whether or not the integral is improper.  </strong> A) The integral is improper. B) The integral is not improper.

A) The integral is improper.
B) The integral is not improper.
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