Deck 6: Techniques of Integration

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

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

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

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

A) <strong>Use the Table of Integrals to evaluate the integral.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use the Table of Integrals to evaluate the integral.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use the Table of Integrals to evaluate the integral.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use the Table of Integrals to evaluate the integral.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use the Table of Integrals to evaluate the integral.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Determine whether the improper integral converges or diverges,and if it converges,find its value. <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A)   B)   C) 15 D) Diverges <div style=padding-top: 35px>

A) <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A)   B)   C) 15 D) Diverges <div style=padding-top: 35px>
B) <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A)   B)   C) 15 D) Diverges <div style=padding-top: 35px>
C) 15
D) Diverges
سؤال
Find the integral. <strong>Find the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Determine whether the improper integral converges or diverges,and if it converges,find its value. <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A)   B) 0 C)   D) Diverges <div style=padding-top: 35px>

A) <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A)   B) 0 C)   D) Diverges <div style=padding-top: 35px>
B) 0
C) <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A)   B) 0 C)   D) Diverges <div style=padding-top: 35px>
D) Diverges
سؤال
Determine whether the improper integral converges or diverges,and if it converges,find its value. <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A) 3 B) 6 C) 0 D) Diverges <div style=padding-top: 35px>

A) 3
B) 6
C) 0
D) Diverges
سؤال
Estimate the area of the shaded region by using the Trapezoidal Rule with n = 4.Round the answer to the nearest tenth. Estimate the area of the shaded region by using the Trapezoidal Rule with n = 4.Round the answer to the nearest tenth.  <div style=padding-top: 35px>
سؤال
Let a and b be real numbers.What integral must appear in place of the question mark "?" to make the following statement true? <strong>Let a and b be real numbers.What integral must appear in place of the question mark ? to make the following statement true?  </strong> A)   B)   C)   D)   E) none of these <div style=padding-top: 35px>

A) <strong>Let a and b be real numbers.What integral must appear in place of the question mark ? to make the following statement true?  </strong> A)   B)   C)   D)   E) none of these <div style=padding-top: 35px>
B) <strong>Let a and b be real numbers.What integral must appear in place of the question mark ? to make the following statement true?  </strong> A)   B)   C)   D)   E) none of these <div style=padding-top: 35px>
C) <strong>Let a and b be real numbers.What integral must appear in place of the question mark ? to make the following statement true?  </strong> A)   B)   C)   D)   E) none of these <div style=padding-top: 35px>
D) <strong>Let a and b be real numbers.What integral must appear in place of the question mark ? to make the following statement true?  </strong> A)   B)   C)   D)   E) none of these <div style=padding-top: 35px>
E) none of these
سؤال
Use the Table of Integrals to evaluate the integral. Use the Table of Integrals to evaluate the integral.  <div style=padding-top: 35px>
سؤال
Evaluate the integral or show that it is divergent. Evaluate the integral or show that it is divergent.  <div style=padding-top: 35px>
سؤال
Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.) <strong>Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Write the form of the partial fraction decomposition of the rational expression.Do not find the numerical values of the constants. <strong>Write the form of the partial fraction decomposition of the rational expression.Do not find the numerical values of the constants.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Write the form of the partial fraction decomposition of the rational expression.Do not find the numerical values of the constants.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Write the form of the partial fraction decomposition of the rational expression.Do not find the numerical values of the constants.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Write the form of the partial fraction decomposition of the rational expression.Do not find the numerical values of the constants.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Write the form of the partial fraction decomposition of the rational expression.Do not find the numerical values of the constants.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.) <strong>Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
A manufacturer of light bulbs wants to produce bulbs that last about 400 hours but,of course,some bulbs burn out faster than others.Let F(t) be the fraction of the company's bulbs that burn out before t hours. F(t) lies between 0 and 1. Let <strong>A manufacturer of light bulbs wants to produce bulbs that last about 400 hours but,of course,some bulbs burn out faster than others.Let F(t) be the fraction of the company's bulbs that burn out before t hours. F(t) lies between 0 and 1. Let   .What is the value of   ?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .What is the value of <strong>A manufacturer of light bulbs wants to produce bulbs that last about 400 hours but,of course,some bulbs burn out faster than others.Let F(t) be the fraction of the company's bulbs that burn out before t hours. F(t) lies between 0 and 1. Let   .What is the value of   ?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> ?

A) <strong>A manufacturer of light bulbs wants to produce bulbs that last about 400 hours but,of course,some bulbs burn out faster than others.Let F(t) be the fraction of the company's bulbs that burn out before t hours. F(t) lies between 0 and 1. Let   .What is the value of   ?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>A manufacturer of light bulbs wants to produce bulbs that last about 400 hours but,of course,some bulbs burn out faster than others.Let F(t) be the fraction of the company's bulbs that burn out before t hours. F(t) lies between 0 and 1. Let   .What is the value of   ?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>A manufacturer of light bulbs wants to produce bulbs that last about 400 hours but,of course,some bulbs burn out faster than others.Let F(t) be the fraction of the company's bulbs that burn out before t hours. F(t) lies between 0 and 1. Let   .What is the value of   ?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>A manufacturer of light bulbs wants to produce bulbs that last about 400 hours but,of course,some bulbs burn out faster than others.Let F(t) be the fraction of the company's bulbs that burn out before t hours. F(t) lies between 0 and 1. Let   .What is the value of   ?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>A manufacturer of light bulbs wants to produce bulbs that last about 400 hours but,of course,some bulbs burn out faster than others.Let F(t) be the fraction of the company's bulbs that burn out before t hours. F(t) lies between 0 and 1. Let   .What is the value of   ?</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Make a substitution to express the integrand as a rational function and then evaluate the integral. Make a substitution to express the integrand as a rational function and then evaluate the integral.   Round the answer to four decimal places.<div style=padding-top: 35px> Round the answer to four decimal places.
سؤال
Use the Table of Integrals to evaluate the integral to three decimal places. Use the Table of Integrals to evaluate the integral to three decimal places.  <div style=padding-top: 35px>
سؤال
Find the integral. <strong>Find the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

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

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

A) <strong>Find the integral using an appropriate trigonometric substitution.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the integral using an appropriate trigonometric substitution.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the integral using an appropriate trigonometric substitution.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the integral using an appropriate trigonometric substitution.  </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 integral. <strong>Find the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find the integral. Find the integral.  <div style=padding-top: 35px>
سؤال
Find the area of the region bounded by the hyperbola Find the area of the region bounded by the hyperbola   and the line  x = 6. <div style=padding-top: 35px> and the line x = 6.
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Evaluate the integral using the indicated trigonometric substitution. Evaluate the integral using the indicated trigonometric substitution.  <div style=padding-top: 35px>
سؤال
Find the integral. Find the integral.  <div style=padding-top: 35px>
سؤال
A particle moves on a straight line with velocity function <strong>A particle moves on a straight line with velocity function   .Find its position function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .Find its position function <strong>A particle moves on a straight line with velocity function   .Find its position function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px> .

A) <strong>A particle moves on a straight line with velocity function   .Find its position function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>A particle moves on a straight line with velocity function   .Find its position function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>A particle moves on a straight line with velocity function   .Find its position function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>A particle moves on a straight line with velocity function   .Find its position function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>A particle moves on a straight line with velocity function   .Find its position function   .</strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>
E) None of these
سؤال
Evaluate the integral using the indicated trigonometric substitution. <strong>Evaluate the integral using the indicated trigonometric substitution.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>

A) <strong>Evaluate the integral using the indicated trigonometric substitution.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
B) <strong>Evaluate the integral using the indicated trigonometric substitution.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
C) <strong>Evaluate the integral using the indicated trigonometric substitution.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
D) <strong>Evaluate the integral using the indicated trigonometric substitution.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
E) <strong>Evaluate the integral using the indicated trigonometric substitution.  </strong> A)   B)   C)   D)   E)   <div style=padding-top: 35px>
سؤال
Evaluate the integral using integration by parts with the indicated choices of u and dv. <strong>Evaluate the integral using integration by parts with the indicated choices of u and dv.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>

A) <strong>Evaluate the integral using integration by parts with the indicated choices of u and dv.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>
B) <strong>Evaluate the integral using integration by parts with the indicated choices of u and dv.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>
C) <strong>Evaluate the integral using integration by parts with the indicated choices of u and dv.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>
D) <strong>Evaluate the integral using integration by parts with the indicated choices of u and dv.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>
E) None of these
سؤال
Household electricity is supplied in the form of alternating current that varies from 170 V to -170 V with a frequency of 60 cycles per second (Hz).The voltage is thus given by the function E(t),where t is the time in seconds.Voltmeters read the RMS (root-mean-square)voltage,which is the square root of the average value of Household electricity is supplied in the form of alternating current that varies from 170 V to -170 V with a frequency of 60 cycles per second (Hz).The voltage is thus given by the function E(t),where t is the time in seconds.Voltmeters read the RMS (root-mean-square)voltage,which is the square root of the average value of   over one cycle.Calculate the RMS voltage of household current.Round your answer to the nearest integer.  <div style=padding-top: 35px> over one cycle.Calculate the RMS voltage of household current.Round your answer to the nearest integer. Household electricity is supplied in the form of alternating current that varies from 170 V to -170 V with a frequency of 60 cycles per second (Hz).The voltage is thus given by the function E(t),where t is the time in seconds.Voltmeters read the RMS (root-mean-square)voltage,which is the square root of the average value of   over one cycle.Calculate the RMS voltage of household current.Round your answer to the nearest integer.  <div style=padding-top: 35px>
سؤال
Find the integral. <strong>Find the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the indefinite integral. <strong>Evaluate the indefinite integral.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>

A) <strong>Evaluate the indefinite integral.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>
B) <strong>Evaluate the indefinite integral.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>
C) <strong>Evaluate the indefinite integral.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>
D) <strong>Evaluate the indefinite integral.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>
E) None of these
سؤال
Find the integral. <strong>Find the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

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

A) <strong>Find the integral using an appropriate trigonometric substitution.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the integral using an appropriate trigonometric substitution.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the integral using an appropriate trigonometric substitution.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the integral using an appropriate trigonometric substitution.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E) None of these <div style=padding-top: 35px>
E) None of these
سؤال
Find the integral. <strong>Find the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

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

A) <strong>Find the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the integral.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
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Deck 6: Techniques of Integration
1
Find the integral. <strong>Find the integral.  </strong> A)   B)   C)   D)

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

A) <strong>Find the integral.  </strong> A)   B)   C)   D)
B) <strong>Find the integral.  </strong> A)   B)   C)   D)
C) <strong>Find the integral.  </strong> A)   B)   C)   D)
D) <strong>Find the integral.  </strong> A)   B)   C)   D)
3
Use a table of integrals to evaluate the integral. <strong>Use a table of integrals to evaluate the integral.  </strong> A)   B)   C)   D)

A) <strong>Use a table of integrals to evaluate the integral.  </strong> A)   B)   C)   D)
B) <strong>Use a table of integrals to evaluate the integral.  </strong> A)   B)   C)   D)
C) <strong>Use a table of integrals to evaluate the integral.  </strong> A)   B)   C)   D)
D) <strong>Use a table of integrals to evaluate the integral.  </strong> A)   B)   C)   D)
4
Use the Table of Integrals to evaluate the integral. <strong>Use the Table of Integrals to evaluate the integral.  </strong> A)   B)   C)   D)   E)

A) <strong>Use the Table of Integrals to evaluate the integral.  </strong> A)   B)   C)   D)   E)
B) <strong>Use the Table of Integrals to evaluate the integral.  </strong> A)   B)   C)   D)   E)
C) <strong>Use the Table of Integrals to evaluate the integral.  </strong> A)   B)   C)   D)   E)
D) <strong>Use the Table of Integrals to evaluate the integral.  </strong> A)   B)   C)   D)   E)
E) <strong>Use the Table of Integrals to evaluate the integral.  </strong> A)   B)   C)   D)   E)
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5
Determine whether the improper integral converges or diverges,and if it converges,find its value. <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A)   B)   C) 15 D) Diverges

A) <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A)   B)   C) 15 D) Diverges
B) <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A)   B)   C) 15 D) Diverges
C) 15
D) Diverges
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6
Find the integral. <strong>Find the integral.  </strong> A)   B)   C)   D)

A) <strong>Find the integral.  </strong> A)   B)   C)   D)
B) <strong>Find the integral.  </strong> A)   B)   C)   D)
C) <strong>Find the integral.  </strong> A)   B)   C)   D)
D) <strong>Find the integral.  </strong> A)   B)   C)   D)
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7
Determine whether the improper integral converges or diverges,and if it converges,find its value. <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A)   B) 0 C)   D) Diverges

A) <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A)   B) 0 C)   D) Diverges
B) 0
C) <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A)   B) 0 C)   D) Diverges
D) Diverges
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8
Determine whether the improper integral converges or diverges,and if it converges,find its value. <strong>Determine whether the improper integral converges or diverges,and if it converges,find its value.  </strong> A) 3 B) 6 C) 0 D) Diverges

A) 3
B) 6
C) 0
D) Diverges
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9
Estimate the area of the shaded region by using the Trapezoidal Rule with n = 4.Round the answer to the nearest tenth. Estimate the area of the shaded region by using the Trapezoidal Rule with n = 4.Round the answer to the nearest tenth.
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10
Let a and b be real numbers.What integral must appear in place of the question mark "?" to make the following statement true? <strong>Let a and b be real numbers.What integral must appear in place of the question mark ? to make the following statement true?  </strong> A)   B)   C)   D)   E) none of these

A) <strong>Let a and b be real numbers.What integral must appear in place of the question mark ? to make the following statement true?  </strong> A)   B)   C)   D)   E) none of these
B) <strong>Let a and b be real numbers.What integral must appear in place of the question mark ? to make the following statement true?  </strong> A)   B)   C)   D)   E) none of these
C) <strong>Let a and b be real numbers.What integral must appear in place of the question mark ? to make the following statement true?  </strong> A)   B)   C)   D)   E) none of these
D) <strong>Let a and b be real numbers.What integral must appear in place of the question mark ? to make the following statement true?  </strong> A)   B)   C)   D)   E) none of these
E) none of these
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11
Use the Table of Integrals to evaluate the integral. Use the Table of Integrals to evaluate the integral.
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12
Evaluate the integral or show that it is divergent. Evaluate the integral or show that it is divergent.
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13
Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.) <strong>Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)  </strong> A)   B)   C)   D)   E)

A) <strong>Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)  </strong> A)   B)   C)   D)   E)
B) <strong>Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)  </strong> A)   B)   C)   D)   E)
C) <strong>Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)  </strong> A)   B)   C)   D)   E)
D) <strong>Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)  </strong> A)   B)   C)   D)   E)
E) <strong>Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)  </strong> A)   B)   C)   D)   E)
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14
Write the form of the partial fraction decomposition of the rational expression.Do not find the numerical values of the constants. <strong>Write the form of the partial fraction decomposition of the rational expression.Do not find the numerical values of the constants.  </strong> A)   B)   C)   D)

A) <strong>Write the form of the partial fraction decomposition of the rational expression.Do not find the numerical values of the constants.  </strong> A)   B)   C)   D)
B) <strong>Write the form of the partial fraction decomposition of the rational expression.Do not find the numerical values of the constants.  </strong> A)   B)   C)   D)
C) <strong>Write the form of the partial fraction decomposition of the rational expression.Do not find the numerical values of the constants.  </strong> A)   B)   C)   D)
D) <strong>Write the form of the partial fraction decomposition of the rational expression.Do not find the numerical values of the constants.  </strong> A)   B)   C)   D)
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15
Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.) <strong>Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)  </strong> A)   B)   C)   D)   E)

A) <strong>Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)  </strong> A)   B)   C)   D)   E)
B) <strong>Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)  </strong> A)   B)   C)   D)   E)
C) <strong>Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)  </strong> A)   B)   C)   D)   E)
D) <strong>Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)  </strong> A)   B)   C)   D)   E)
E) <strong>Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)  </strong> A)   B)   C)   D)   E)
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16
A manufacturer of light bulbs wants to produce bulbs that last about 400 hours but,of course,some bulbs burn out faster than others.Let F(t) be the fraction of the company's bulbs that burn out before t hours. F(t) lies between 0 and 1. Let <strong>A manufacturer of light bulbs wants to produce bulbs that last about 400 hours but,of course,some bulbs burn out faster than others.Let F(t) be the fraction of the company's bulbs that burn out before t hours. F(t) lies between 0 and 1. Let   .What is the value of   ?</strong> A)   B)   C)   D)   E)   .What is the value of <strong>A manufacturer of light bulbs wants to produce bulbs that last about 400 hours but,of course,some bulbs burn out faster than others.Let F(t) be the fraction of the company's bulbs that burn out before t hours. F(t) lies between 0 and 1. Let   .What is the value of   ?</strong> A)   B)   C)   D)   E)   ?

A) <strong>A manufacturer of light bulbs wants to produce bulbs that last about 400 hours but,of course,some bulbs burn out faster than others.Let F(t) be the fraction of the company's bulbs that burn out before t hours. F(t) lies between 0 and 1. Let   .What is the value of   ?</strong> A)   B)   C)   D)   E)
B) <strong>A manufacturer of light bulbs wants to produce bulbs that last about 400 hours but,of course,some bulbs burn out faster than others.Let F(t) be the fraction of the company's bulbs that burn out before t hours. F(t) lies between 0 and 1. Let   .What is the value of   ?</strong> A)   B)   C)   D)   E)
C) <strong>A manufacturer of light bulbs wants to produce bulbs that last about 400 hours but,of course,some bulbs burn out faster than others.Let F(t) be the fraction of the company's bulbs that burn out before t hours. F(t) lies between 0 and 1. Let   .What is the value of   ?</strong> A)   B)   C)   D)   E)
D) <strong>A manufacturer of light bulbs wants to produce bulbs that last about 400 hours but,of course,some bulbs burn out faster than others.Let F(t) be the fraction of the company's bulbs that burn out before t hours. F(t) lies between 0 and 1. Let   .What is the value of   ?</strong> A)   B)   C)   D)   E)
E) <strong>A manufacturer of light bulbs wants to produce bulbs that last about 400 hours but,of course,some bulbs burn out faster than others.Let F(t) be the fraction of the company's bulbs that burn out before t hours. F(t) lies between 0 and 1. Let   .What is the value of   ?</strong> A)   B)   C)   D)   E)
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17
Make a substitution to express the integrand as a rational function and then evaluate the integral. Make a substitution to express the integrand as a rational function and then evaluate the integral.   Round the answer to four decimal places. Round the answer to four decimal places.
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18
Use the Table of Integrals to evaluate the integral to three decimal places. Use the Table of Integrals to evaluate the integral to three decimal places.
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19
Find the integral. <strong>Find the integral.  </strong> A)   B)   C)   D)

A) <strong>Find the integral.  </strong> A)   B)   C)   D)
B) <strong>Find the integral.  </strong> A)   B)   C)   D)
C) <strong>Find the integral.  </strong> A)   B)   C)   D)
D) <strong>Find the integral.  </strong> A)   B)   C)   D)
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20
Evaluate the integral. Evaluate the integral.
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21
Find the integral. <strong>Find the integral.  </strong> A)   B)   C)   D)

A) <strong>Find the integral.  </strong> A)   B)   C)   D)
B) <strong>Find the integral.  </strong> A)   B)   C)   D)
C) <strong>Find the integral.  </strong> A)   B)   C)   D)
D) <strong>Find the integral.  </strong> A)   B)   C)   D)
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22
Find the integral using an appropriate trigonometric substitution. <strong>Find the integral using an appropriate trigonometric substitution.  </strong> A)   B)   C)   D)

A) <strong>Find the integral using an appropriate trigonometric substitution.  </strong> A)   B)   C)   D)
B) <strong>Find the integral using an appropriate trigonometric substitution.  </strong> A)   B)   C)   D)
C) <strong>Find the integral using an appropriate trigonometric substitution.  </strong> A)   B)   C)   D)
D) <strong>Find the integral using an appropriate trigonometric substitution.  </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
Find the integral. <strong>Find the integral.  </strong> A)   B)   C)   D)

A) <strong>Find the integral.  </strong> A)   B)   C)   D)
B) <strong>Find the integral.  </strong> A)   B)   C)   D)
C) <strong>Find the integral.  </strong> A)   B)   C)   D)
D) <strong>Find the integral.  </strong> A)   B)   C)   D)
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25
Find the integral. Find the integral.
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26
Find the area of the region bounded by the hyperbola Find the area of the region bounded by the hyperbola   and the line  x = 6. and the line x = 6.
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27
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E)

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E)
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E)
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E)
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E)
E) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E)
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28
Evaluate the integral using the indicated trigonometric substitution. Evaluate the integral using the indicated trigonometric substitution.
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29
Find the integral. Find the integral.
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30
A particle moves on a straight line with velocity function <strong>A particle moves on a straight line with velocity function   .Find its position function   .</strong> A)   B)   C)   D)   E)   .Find its position function <strong>A particle moves on a straight line with velocity function   .Find its position function   .</strong> A)   B)   C)   D)   E)   .

A) <strong>A particle moves on a straight line with velocity function   .Find its position function   .</strong> A)   B)   C)   D)   E)
B) <strong>A particle moves on a straight line with velocity function   .Find its position function   .</strong> A)   B)   C)   D)   E)
C) <strong>A particle moves on a straight line with velocity function   .Find its position function   .</strong> A)   B)   C)   D)   E)
D) <strong>A particle moves on a straight line with velocity function   .Find its position function   .</strong> A)   B)   C)   D)   E)
E) <strong>A particle moves on a straight line with velocity function   .Find its position function   .</strong> A)   B)   C)   D)   E)
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31
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E) None of these

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E) None of these
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E) None of these
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E) None of these
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E) None of these
E) None of these
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32
Evaluate the integral using the indicated trigonometric substitution. <strong>Evaluate the integral using the indicated trigonometric substitution.  </strong> A)   B)   C)   D)   E)

A) <strong>Evaluate the integral using the indicated trigonometric substitution.  </strong> A)   B)   C)   D)   E)
B) <strong>Evaluate the integral using the indicated trigonometric substitution.  </strong> A)   B)   C)   D)   E)
C) <strong>Evaluate the integral using the indicated trigonometric substitution.  </strong> A)   B)   C)   D)   E)
D) <strong>Evaluate the integral using the indicated trigonometric substitution.  </strong> A)   B)   C)   D)   E)
E) <strong>Evaluate the integral using the indicated trigonometric substitution.  </strong> A)   B)   C)   D)   E)
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33
Evaluate the integral using integration by parts with the indicated choices of u and dv. <strong>Evaluate the integral using integration by parts with the indicated choices of u and dv.  </strong> A)   B)   C)   D)   E) None of these

A) <strong>Evaluate the integral using integration by parts with the indicated choices of u and dv.  </strong> A)   B)   C)   D)   E) None of these
B) <strong>Evaluate the integral using integration by parts with the indicated choices of u and dv.  </strong> A)   B)   C)   D)   E) None of these
C) <strong>Evaluate the integral using integration by parts with the indicated choices of u and dv.  </strong> A)   B)   C)   D)   E) None of these
D) <strong>Evaluate the integral using integration by parts with the indicated choices of u and dv.  </strong> A)   B)   C)   D)   E) None of these
E) None of these
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34
Household electricity is supplied in the form of alternating current that varies from 170 V to -170 V with a frequency of 60 cycles per second (Hz).The voltage is thus given by the function E(t),where t is the time in seconds.Voltmeters read the RMS (root-mean-square)voltage,which is the square root of the average value of Household electricity is supplied in the form of alternating current that varies from 170 V to -170 V with a frequency of 60 cycles per second (Hz).The voltage is thus given by the function E(t),where t is the time in seconds.Voltmeters read the RMS (root-mean-square)voltage,which is the square root of the average value of   over one cycle.Calculate the RMS voltage of household current.Round your answer to the nearest integer.  over one cycle.Calculate the RMS voltage of household current.Round your answer to the nearest integer. Household electricity is supplied in the form of alternating current that varies from 170 V to -170 V with a frequency of 60 cycles per second (Hz).The voltage is thus given by the function E(t),where t is the time in seconds.Voltmeters read the RMS (root-mean-square)voltage,which is the square root of the average value of   over one cycle.Calculate the RMS voltage of household current.Round your answer to the nearest integer.
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35
Find the integral. <strong>Find the integral.  </strong> A)   B)   C)   D)

A) <strong>Find the integral.  </strong> A)   B)   C)   D)
B) <strong>Find the integral.  </strong> A)   B)   C)   D)
C) <strong>Find the integral.  </strong> A)   B)   C)   D)
D) <strong>Find the integral.  </strong> A)   B)   C)   D)
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36
Evaluate the indefinite integral. <strong>Evaluate the indefinite integral.  </strong> A)   B)   C)   D)   E) None of these

A) <strong>Evaluate the indefinite integral.  </strong> A)   B)   C)   D)   E) None of these
B) <strong>Evaluate the indefinite integral.  </strong> A)   B)   C)   D)   E) None of these
C) <strong>Evaluate the indefinite integral.  </strong> A)   B)   C)   D)   E) None of these
D) <strong>Evaluate the indefinite integral.  </strong> A)   B)   C)   D)   E) None of these
E) None of these
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37
Find the integral. <strong>Find the integral.  </strong> A)   B)   C)   D)

A) <strong>Find the integral.  </strong> A)   B)   C)   D)
B) <strong>Find the integral.  </strong> A)   B)   C)   D)
C) <strong>Find the integral.  </strong> A)   B)   C)   D)
D) <strong>Find the integral.  </strong> A)   B)   C)   D)
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38
Find the integral using an appropriate trigonometric substitution. <strong>Find the integral using an appropriate trigonometric substitution.  </strong> A)   B)   C)   D)

A) <strong>Find the integral using an appropriate trigonometric substitution.  </strong> A)   B)   C)   D)
B) <strong>Find the integral using an appropriate trigonometric substitution.  </strong> A)   B)   C)   D)
C) <strong>Find the integral using an appropriate trigonometric substitution.  </strong> A)   B)   C)   D)
D) <strong>Find the integral using an appropriate trigonometric substitution.  </strong> A)   B)   C)   D)
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39
Evaluate the integral. <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E) None of these

A) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E) None of these
B) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E) None of these
C) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E) None of these
D) <strong>Evaluate the integral.  </strong> A)   B)   C)   D)   E) None of these
E) None of these
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40
Find the integral. <strong>Find the integral.  </strong> A)   B)   C)   D)

A) <strong>Find the integral.  </strong> A)   B)   C)   D)
B) <strong>Find the integral.  </strong> A)   B)   C)   D)
C) <strong>Find the integral.  </strong> A)   B)   C)   D)
D) <strong>Find the integral.  </strong> A)   B)   C)   D)
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41
Evaluate the integral. Evaluate the integral.
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42
Evaluate the following integralEvaluate the following integral
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43
Find the integral. <strong>Find the integral.  </strong> A)   B)   C)   D)

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