Deck 7: Integration Techniques

Question 1

Evaluate the integral.

A)
B)
C)
D)

Answer 1

C

Question 2

Evaluate the integral.

A)
B)
C)
D)

Answer 2

A

Question 3

Evaluate the integral.

A)
B)
C)
D)

Answer 3

A

Question 4

Evaluate the integral.

A)
B)
C)
D)

Question 5

Evaluate the integral.

A)
B)
C)
D)

Question 6

Evaluate the integral.

A)
B)
C)
D)

Question 7

Evaluate the integral.

A)
B)
C)
D)

Question 8

Evaluate the integral.

A)
B)
C)
D)

Question 9

Evaluate the integral.

A)
B)
C)
D)

Question 10

Evaluate the integral.

A)
B)
C)
D)

Question 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). and

A)
B)
C)
D)

Question 12

Evaluate the integral.

A)
B)
C)
D)

Question 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).

A)
B)
C)
D)

Question 14

Evaluate the integral.

A)
B)
C)
D)

Question 15

Evaluate the integral.

A)
B)
C)
D)

Question 16

Find where

A)
B)
C)
D)

Question 17

Find

A)
B)
C)
D)

Question 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). and

A)
B)
C)
D)

Question 19

Evaluate the integral.

A)
B)
C)
D)

Question 20

Evaluate the integral.

A)
B)
C)
D)

Question 21

Evaluate the integral. (Hint: you may need to use a reduction formula.)

A)
B)
C)
D)

Question 22

Evaluate the integral.

A)
B)
C)
D)

Question 23

Evaluate the integral.

A)
B)
C)
D)

Question 24

Evaluate the integral.

A)
B)
C)
D)

Question 25

Evaluate the integral using integration by parts and substitution.

A)
B)
C)
D)

Question 26

Evaluate the integral using integration by parts and substitution (as we recommended in the text, "Try something!").

A)
B)
C)
D)

Question 27

Evaluate the integral.

A)
B)
C)
D)

Question 28

Evaluate the integral.

Question 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 , (Use integration by parts with ).

Question 30

Evaluate the integral.

A)
B)
C)
D)

Question 31

Evaluate the integral.

A)
B)
C)
D)

Question 32

Evaluate the integral.

A)
B)
C)
D)

Question 33

Evaluate the integral. (Hint: you may need to use a reduction formula.)

A)
B)
C)
D)

Question 34

Evaluate the integral using integration by parts and substitution (as we recommended in the text, "Try something!").

A)
B)
C)
D)

Question 35

Evaluate the integral. (Hint: you may need to use a reduction formula.)

A)
B)
C)
D)

Question 36

Evaluate the integral.

A)
B)
C)
D)

Question 37

Evaluate the integral.

A)
B)
C)
D)

Question 38

Evaluate the integral.

A)
B)
C)
D)

Question 39

Evaluate the integral.

A)
B)
C)
D)

Question 40

Evaluate the integral.

A)
B)
C)
D)

Question 41

Find an antiderivative.

A)
B)
C)
D)

Question 42

Evaluate the integral.

A)
B)
C)
D)

Question 43

Find the partial fraction decomposition.

A)
B)
C)
D)

Question 44

Find an antiderivative.

A)
B)
C)
D)

Question 45

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

A)
B)
C)
D)

Question 46

Evaluate the integral.

A)
B)
C)
D)

Question 47

Find an antiderivative.

A)
B)
C)
D)

Question 48

Find the partial fraction decomposition.

A)
B)
C)
D)

Question 49

Evaluate the integral.

A)
B)
C)
D)

Question 50

Evaluate the integral.

Question 51

Find the partial fraction decomposition.

A)
B)
C)
D)

Question 52

Evaluate the integral.

A)
B)
C)
D)

Question 53

Evaluate the integral.

A)
B)
C)
D)

Question 54

Find an antiderivative.

A)
B)
C)
D)

Question 55

Evaluate the integral.

A)
B)
C)
D)

Question 56

Find the partial fraction decomposition.

A)
B)
C)
D)

Question 57

Find the partial fraction decomposition.

A)
B)
C)
D)

Question 58

Find an antiderivative.

A)
B)
C)
D)

Question 59

Find an antiderivative.

A)
B)
C)
D)

Question 60

Find the partial fraction decomposition.

A)
B)
C)
D)

Question 61

Use a table of integrals to find an antiderivative.

A)
B)
C)
D)

Question 62

Find the partial fraction decomposition.

A)
B)
C)
D)

Question 63

Evaluate the integral.

A)
B)
C)
D)

Question 64

Find the partial fraction decomposition.

A)
B)
C)
D)

Question 65

Find the partial fraction decomposition.

A)
B)
C)
D)

Question 66

Determine whether or not the integral is improper.

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

Question 67

Find the partial fractions decomposition and an antiderivative.

Question 68

Use a table of integrals to find an antiderivative.

A)
B)
C)
D)

Question 69

Determine whether the integral converges or diverges. Find the value of the integral if it converges.

A) The integral diverges.
B) The integral evaluates to .
C) The integral evaluates to .
D) The integral evaluates to .

Question 70

Determine whether the integral converges or diverges. Find the value of the integral if it converges.

A) The integral diverges.
B) The integral evaluates to .
C) The integral evaluates to .
D) The integral evaluates to .

Question 71

Use a table of integrals to evaluate the definite integral.

A)
B)
C)
D)

Question 72

Evaluate the integral.

A)
B)
C)
D)

Question 73

Determine whether or not the integral is improper.

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

Question 74

Use a table of integrals to find an antiderivative.

A)
B)
C)
D)

Question 75

Use a table of integrals to find an antiderivative.

A)
B)
C)
D)

Question 76

Use an integral formula to evaluate the integral.

A)
B)
C)
D)

Question 77

Use a table of integrals to find an antiderivative.

A)
B)
C)
D)

Question 78

Use a table of integrals to find an antiderivative.

A)
B)
C)
D)

Question 79

Use a table of integrals to find an antiderivative.

A)
B)
C)
D)

Question 80

Determine whether or not the integral is improper.

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