Question 1

To evaluate the integral  using Integration by Parts, we should choose:

Accepted Answer

To use Integration by Parts, we should choose the function that will differentiate to become simpler and the function that will integrate to become simpler. The function 11eaa655_3b04_ea0f_a696_f36c5ae3183a_TB5596_11 has a derivative of e^(-x) which becomes simpler with every differentiation, and has an antiderivative of (-1/2)e^(-x^2) which becomes simpler with every integration. Therefore, choice B is the best option to evaluate the integral using Integration by Parts.

Question 2

To evaluate the integral  using integration by parts, the convenient choice is :

Accepted Answer

D

Question 3

Evaluate the integral using one or two methods, as indicated.
A)  : the Substitution Method followed by Integration by Parts, twice. 
B)  : Integration by Parts followed by the Substitution Method.

Accepted Answer

A)  B)

Question 4

Use the substitution  and the trigonometric identity  to evaluate the integral.

Accepted Answer

The answer of Use the substitution  and the trigonometric...

Question 5

Compute the integrals using the reduction formulas, or the substitution  , and the identities  ,  , as required. 
A)  
B)

Accepted Answer

The answer of Compute the integrals using the reduction formulas,...

Question 6

Compute the integral  .

Accepted Answer

The answer of Compute the integral  ....

Question 7

Evaluate the integrals using Integration by Parts, the Substitution Method, or both methods.
A)  
B)

Accepted Answer

The answer of Evaluate the integrals using Integration by Parts,...

Question 8

Compute the following integrals.
A)  
B)

Accepted Answer

The answer of Compute the following integrals.
A)  
B) ...

Question 9

For computing the integral  , the most efficient method is

Accepted Answer

The answer of For computing the integral  , the...

Question 10

The value of the integral  is:

Accepted Answer

The answer of The value of the integral  is:
...

Question 11

Use the substitution  and the trigonometric identity  , or reduction formulas as necessary, to calculate the integrals. 
A)  
B)

Accepted Answer

The answer of Use the substitution  and the trigonometric...

Question 12

Evaluate the integral  .

Accepted Answer

Taking the integral of e^x dx results in e^x + C, where C is the constant of integration. Therefore, the answer to this integral would be 11e^x + C. However, since we are evaluating the integral within a specified domain, the constant of integration will cancel out. Therefore, the answer is simply 11e^a696. Choice C is the only option with "5f4b" in the answer, which matches the given integral.

Question 13

Compute the integral  .

Accepted Answer

The answer of Compute the integral  ....

Question 14

Evaluate the integrals using Integration by Parts, the Substitution Method, or both methods.
A)  
B)  . (Hint: Use  .

Accepted Answer

The answer of Evaluate the integrals using Integration by Parts,...

Question 15

To evaluate the integral  by Integration by Parts, the convenient choice is

Accepted Answer

The answer of To evaluate the integral  by Integration...

Question 16

Evaluate the integrals.
A)  
B)

Accepted Answer

The answer of Evaluate the integrals.
A)  
B) ...

Question 17

To evaluate the integral  using Integration by Parts, we should choose:

Accepted Answer

The answer of To evaluate the integral  using Integration...

Question 18

Evaluate the integral

Accepted Answer

The answer of Evaluate the integral ...

Question 19

Evaluate the integral  .

Accepted Answer

The answer of Evaluate the integral  ....

Question 20

Which of the following methods is efficient in computing the integral  ?

Accepted Answer

The answer of Which of the following methods is efficient...

Quiz 8: Techniques of Integration

To evaluate the integral using Integration by Parts, we should choose:

To evaluate the integral using integration by parts, the convenient choice is :

Evaluate the integral using one or two methods, as indicated. A) : the Substitution Method followed by Integration by Parts, twice. B) : Integration by Parts followed by the Substitution Method.

Use the substitution and the trigonometric identity to evaluate the integral.

Compute the integrals using the reduction formulas, or the substitution , and the identities , , as required. A) B)

Compute the integral .

Evaluate the integrals using Integration by Parts, the Substitution Method, or both methods. A) B)

Compute the following integrals. A) B)

For computing the integral , the most efficient method is

The value of the integral is:

Use the substitution and the trigonometric identity , or reduction formulas as necessary, to calculate the integrals. A) B)

Evaluate the integral .

Compute the integral .

Evaluate the integrals using Integration by Parts, the Substitution Method, or both methods. A) B) . (Hint: Use .

To evaluate the integral by Integration by Parts, the convenient choice is

Evaluate the integrals. A) B)

To evaluate the integral using Integration by Parts, we should choose:

Evaluate the integral

Evaluate the integral .

Which of the following methods is efficient in computing the integral ?