Deck 7: Techniques of Integration

Question 1

Evaluate the integral.

Answer 1

Question 2

Evaluate the following integral.

Answer 2

Question 3

Evaluate the integral.

Answer 3

Question 4

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

Question 5

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

Question 6

Evaluate the integral to six decimal places.

Question 7

Evaluate the integral.

Question 8

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

Question 9

Find the integral.

Question 10

Eight milligrams of a dye are injected into a vein leading the an individual's heart.The concentration of dye in the aorta (in milligrams per liter) measured at 2-sec intervals is shown in the accompanying table.Use Simpson's Rule with and the formula to estimate the person's cardiac output, where is the quantity of dye injected in milligrams, is the concentration of the dye in the aorta, and is measured in liters per minute.Round to one decimal place.

Question 11

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

Question 12

The region under the graph of on the interval [1, 2] is revolved about the Find the volume of the resulting solid.

Question 13

Find the integral.

Question 14

Find a bound on the error in approximating the integral using (a) the Trapezoidal Rule and (b) Simpson's Rule with ubintervals.

Question 15

Evaluate the integral.

Question 16

Use the Trapezoidal Rule to approximate for Round the result to four decimal places.

Question 17

Use (a) the Trapezoidal Rule and (b) Simpson's Rule to approximate the integral to four decimal places.Compare your results with the exact value.

Question 18

Use the Table of Integrals to evaluate the integral.

Question 19

A body moves along a coordinate line in such a way that its velocity at any time , where is given by Find its position function if it is initially located at the origin.

Question 20

Evaluate the integral using an appropriate trigonometric substitution.

Question 21

Evaluate the integral.

Question 22

Evaluate the integral or show that it is divergent.

Question 23

Evaluate the integral.

Question 24

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

Question 25

Evaluate the integral.

Question 26

Estimate the area of the shaded region by using the Trapezoidal Rule with Round theAnswer to the nearest tenth.

Question 27

Evaluate the integral.

Question 28

Evaluate the integral to six decimal places.

Question 29

Find the volume of the resulting solid if the region under the curve from to is rotated about the x-axis.Round yourAnswer to four decimal places.

Question 30

Evaluate the integral.

Question 31

Evaluate the integral using the indicated trigonometric substitution.

Question 32

Find the integral.

Question 33

Find the area bounded by the curves and between and

Question 34

Evaluate the integral.

Question 35

Evaluate the integral.

Question 36

Evaluate the integral.

Question 37

Evaluate the integral using an appropriate trigonometric substitution.

Question 38

Find the integral using an appropriate trigonometric substitution.

Question 39

Evaluate the integral.

Question 40

Find a bound on the error in approximating the integral using (a) the Trapezoidal Rule and (b) Simpson's Rule with subintervals.

Question 41

Select the correct Answer for each question.
Evaluate the integral using integration by parts with the indicated choices of and

A)
B)
C)
D)
E)

Question 42

Select the correct Answer for each question.
Find the integral.

A)
B)
C)
D)

Question 43

Select the correct Answer for each question.
Use a table of integrals to evaluate the integral.

A)
B)
C)
D)

Question 44

Select the correct Answer for each question.
Evaluate the integral.

A)
B)
C)
D)
E)

Question 45

Select the correct Answer for each question.
Evaluate the integral.

A)
B)
C)
D)
E)None of these

Question 46

Select the correct Answer for each question.
Find the integral.

A)
B)
C)
D)

Question 47

Select the correct Answer for each question.
A particle moves on a straight line with velocity function Find its position function

A)
B)
C)
D)
E)

Question 48

Select the correct Answer for each question.
Evaluate the integral.

A)
B)
C)
D)
E)

Question 49

Select the correct Answer for each question.
Use a table of integrals to evaluate the integral.

A)
B)
C)
D)

Question 50

Select the correct Answer for each question.
Find the integral.

A)
B)
C)
D)

Question 51

Select the correct Answer for each question.
Let and be real numbers.What integral must appear in place of the question mark "?" to make the following statement true?

A)
B)
C)
D)
E)

Question 52

Select the correct Answer for each question.
Evaluate the integral.

A)
B)Ф
C)
D)
E)

Question 53

Select the correct Answer for each question.
Find the average value of the function in the interval

A)
B)
C)
D)
E)

Question 54

Select the correct Answer for each question.
Determine whether the improper integral converges or diverges, and if it converges, find its value.

A)15
B)
C)Diverges
D)

Question 55

Select the correct Answer for each question.
Evaluate the integral or show that it is divergent.

A)
B)
C)
D)
E)

Question 56

Select the correct Answer for each question.
Find the integral.

A)
B)
C)
D)

Question 57

Select the correct Answer for each question.
Use long division to evaluate the integral.

A)
B)
C)
D)
E)

Question 58

Select the correct Answer for each question.
Use long division to evaluate the integral. The choices are rounded to 3 decimal places.

A)
B)
C)
D)
E)

Question 59

Select the correct Answer for each question.
Evaluate the integral.

A)
B)
C)
D)

Question 60

Select the correct Answer for each question.
Use a table of integrals to evaluate the integral.

A)
B)
C)
D)

Question 61

Select the correct Answer for each question.
Use long division to evaluate the integral. The choices are rounded to 3 decimal places.

A)
B)
C)
D)
E)

Question 62

Select the correct Answer for each question.
Use a table of integrals to evaluate the integral.

A)
B)
C)
D)

Question 63

Select the correct Answer for each question.
Evaluate the integral using the indicated trigonometric substitution.

A)
B)
C)
D)
E)

Question 64

Select the correct Answer for each question.
Evaluate the integral.

A)
B) Ф
C)
D)
E)

Question 65

Select the correct Answer for each question.
Use the Trapezoidal Rule to approximate the integral withAnswers rounded to four decimal places.

A)0.2029
B)0.1088
C)0.1163
D)0.2326

Question 66

Select the correct Answer for each question.
Find the area bounded by the curves and between and

A)
B)
C)
D)
E)

Question 67

Select the correct Answer for each question.
Find the integral.

A)
B)
C)
D)

Question 68

Select the correct Answer for each question.
Evaluate the integral.

A)
B)
C)
D)
E)

Question 69

Select the correct Answer for each question.
Evaluate the integral.

A)
B)
C)
D)
E)

Question 70

Select the correct Answer for each question.
Evaluate the integral.

A)
B)
C)
D)
E)

Question 71

Select the correct Answer for each question.
Use a table of integrals to evaluate the integral.

A)
B)
C)
D)

Question 72

Select the correct Answer for each question.
Find the integral.

A)
B)
C)
D)

Question 73

Select the correct Answer for each question.
Use Simpson's Rule to approximate the integral withAnswers rounded to four decimal places.

A)2.0076
B)2.9504
C)2.6098
D)2.2955

Question 74

Select the correct Answer for each question.
Evaluate the integral.

A)
B)
C)
D)

Question 75

Select the correct Answer for each question.
The region is represented below.Find the area of this region to two decimal places.

A)20.28
B)
C)
D)
E)

Question 76

Select the correct Answer for each question.
Evaluate the integral using an appropriate trigonometric substitution.

A)
B)
C)
D)

Question 77

Select the correct Answer for each question.
Evaluate the integral.

A)
B)
C)
D)
E)None of these

Question 78

Select the correct Answer for each question.
Evaluate the integral.

A)
B)6.5700
C)0.7166
D)11.8665
E)

Question 79

Select the correct Answer for each question.
Evaluate the integral using integration by parts with the indicated choices of u and dv.

A)
B)
C)
D)
E)

Question 80

Select the correct Answer for each question.
Find the integral.

A)
B)
C)
D)