Deck 7: Techniques of Integration

Question 1

Answer 1

Question 2

Use the Table of Integrals to evaluate the integral to three decimal places.

Answer 2

Question 3

Evaluate the integral using an appropriate trigonometric substitution.

Answer 3

Question 4

Find the integral.

Question 5

Evaluate the integral.

Question 6

Evaluate the integral.

Question 7

The region under the graph of

Question 8

Evaluate the integral.

Question 9

Evaluate the following integral.

Question 10

Question 11

Use the Table of Integrals to evaluate the integral.

Question 12

Evaluate the integral to six decimal places.

Question 13

Question 14

Evaluate the integral.

Question 15

Find the integral.

Question 16

Question 17

Determine whether the improper integral converges or diverges, and if it converges, find its value.

Question 18

Question 19

Determine whether the integral converges or diverges.If it converges, find its value.

Question 20

Make a substitution to express the integrand as a rational function and then evaluate the integral. Round the answer to four decimal places.

Question 21

Evaluate the integral.

Question 22

Evaluate the integral using an appropriate trigonometric substitution.

Question 23

Evaluate the integral.

Question 24

Evaluate the integral.

Question 25

Evaluate the integral using the indicated trigonometric substitution.

Question 26

Find the integral.

Question 27

Make a substitution to express the integrand as a rational function and then evaluate the integral. Round the answer to four decimal places.

Question 28

Question 29

Find the integral using an appropriate trigonometric substitution.

Question 30

Question 31

Evaluate the integral to six decimal places.

Question 32

Evaluate the integral.

Question 33

Evaluate the integral.

Question 34

Evaluate the integral.

Question 35

Evaluate the integral.

Question 36

Evaluate the integral or show that it is divergent.

Question 37

Evaluate the integral.

Question 38

Evaluate the integral.

Question 39

Question 40

Find the volume of the resulting solid if the region under the curve

Question 41

Question 42

Evaluate the integral.

Question 43

Question 44

Find the integral.

Question 45

Question 46

Question 47

Question 48

Evaluate the integral.

Question 49

Use a table of integrals to evaluate the integral.

Question 50

Question 51

Evaluate the integral using integration by parts with the indicated choices of u and dv.

Question 52

Use long division to evaluate the integral.

Question 53

Evaluate the integral or show that it is divergent.

Question 54

Use a table of integrals to evaluate the integral.

Question 55

Question 56

Determine whether the improper integral converges or diverges, and if it converges, find its value.

Question 57

Evaluate the integral.

Question 58

Question 59

Evaluate the integral.

Question 60

Find the integral.

Question 61

Find the integral.

Question 62

Use long division to evaluate the integral. The choices are rounded to 3 decimal places.

Question 63

Question 64

Use a table of integrals to evaluate the integral.

Question 65

Use a table of integrals to evaluate the integral.

Question 66

Find the integral.

Question 67

Evaluate the integral using the indicated trigonometric substitution.

Question 68

Evaluate the integral.

Question 69

Use Simpson's Rule to approximate the integral with answers rounded to four decimal places.

Question 70

Use the Trapezoidal Rule to approximate the integral with answers rounded to four decimal places.

Question 71

Evaluate the integral.

Question 72

Evaluate the integral.

Question 73

Evaluate the integral.

Question 74

Evaluate the integral.

Question 75

Question 76

Evaluate the integral using an appropriate trigonometric substitution.

Question 77

Evaluate the integral.

Question 78

Question 79