Deck 8: Integration Techniques

Question 1

Evaluate the integral.

A)
B)
C)
D)

Answer 1

Question 2

Evaluate the integral.

A)
B)
C)
D)

Answer 2

Question 3

Evaluate the integral.

A)
B)
C)
D)

Answer 3

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

Find

A)
B)
C)
D)

Question 8

Evaluate the integral.

A)
B)
C)
D)

Question 9

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 10

Evaluate the integral.

A)
B)
C)
D)

Question 11

Find where

A)
B)
C)
D)

Question 12

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 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

Evaluate the integral.

A)
B)
C)
D)

Question 17

Evaluate the integral.

A)
B)
C)
D)

Question 18

Evaluate the integral.

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.

Question 23

Evaluate the integral.

A)
B)
C)
D)

Question 24

Evaluate the integral.

A)
B)
C)
D)

Question 25

Evaluate the integral.

A)
B)
C)
D)

Question 26

Evaluate the integral.

A)
B)
C)
D)

Question 27

Evaluate the integral.

A)
B)
C)
D)

Question 28

Evaluate the integral.

A)
B)
C)
D)

Question 29

Evaluate the integral.

A)
B)
C)
D)

Question 30

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

A)
B)
C)
D)

Question 31

Evaluate the integral.

A)
B)
C)
D)

Question 32

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

A)
B)
C)
D)

Question 33

Evaluate the integral.

A)
B)
C)
D)

Question 34

Evaluate the integral.

A)
B)
C)
D)

Question 35

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

A)
B)
C)
D)

Question 36

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

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 using integration by parts and substitution.

A)
B)
C)
D)

Question 40

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 41

Find an antiderivative.

A)
B)
C)
D)

Question 42

Find an antiderivative.

A)
B)
C)
D)

Question 43

Find the partial fraction decomposition.

A)
B)
C)
D)

Question 44

Find the partial fraction decomposition.

A)
B)
C)
D)

Question 45

Find an antiderivative.

A)
B)
C)
D)

Question 46

Evaluate the integral.

A)
B)
C)
D)

Question 47

Find the partial fraction decomposition.

A)
B)
C)
D)

Question 48

Evaluate the integral.

A)
B)
C)
D)

Question 49

Find an antiderivative.

A)
B)
C)
D)

Question 50

Find the partial fraction decomposition.

A)
B)
C)
D)

Question 51

Evaluate the integral.

Question 52

Find the partial fraction decomposition.

A)
B)
C)
D)

Question 53

Find an antiderivative.

A)
B)
C)
D)

Question 54

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 55

Evaluate the integral.

A)
B)
C)
D)

Question 56

Find an antiderivative.

A)
B)
C)
D)

Question 57

Evaluate the integral.

A)
B)
C)
D)

Question 58

Evaluate the integral.

A)
B)
C)
D)

Question 59

Evaluate the integral.

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

Use a table of integrals to find an antiderivative.

A)
B)
C)
D)

Question 63

Find the partial fractions decomposition and an antiderivative.

Question 64

Find the limit.

A) 1
B) 8
C)
D)

Question 65

Find the indicated limit.

A) 0
B)
C)
D) does not exist

Question 66

Use a table of integrals to find an antiderivative.

A)
B)
C)
D)

Question 67

Find the indicated limit.

A) 0
B)
C)
D) limit does not exist

Question 68

Evaluate the integral.

A)
B)
C)
D)

Question 69

Find the limit.

A) 0
B) 1
C) -3
D) 3

Question 70

Use an integral formula to evaluate the integral.

A)
B)
C)
D)

Question 71

Find the partial fraction decomposition.

A)
B)
C)
D)

Question 72

Evaluate the integral.

A)
B)
C)
D)

Question 73

Use a table of integrals to evaluate the definite integral.

A)
B)
C)
D)

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 a table of integrals to find an antiderivative.

A)
B)
C)
D)

Question 77

Use a table of integrals to find an antiderivative.

A)
B)
C)
D)

Question 78

Find the partial fraction decomposition.

A)
B)
C)
D)

Question 79

Find the partial fraction decomposition.

A)
B)
C)
D)

Question 80

Find the limit.

A) 0
B) 1
C)
D)