Stewart - Calculus ET 8e Chapter 7 Form A
1. Evaluate the integral.
2. Evaluate the integral.
3. Evaluate the following integral.
4. Evaluate the integral to six decimal places.
5. Evaluate the integral.
6. Make a substitution to express the integrand as a rational function and then evaluate the integral.
Round the answer to four decimal places.
7. Use the Table of Integrals to evaluate the integral to three decimal places.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 7 Form A
8. Use the Table of Integrals to evaluate the integral.
9. Use the Trapezoidal Rule to approximate
for
. Round the result to four decimal
places.
10. Determine whether the integral converges or diverges. If it converges, find its value.
11. Find the integral.
12. Evaluate the integral using an appropriate trigonometric substitution.
13. Find the integral.
14. The region under the graph of
on the interval [1, 2] is revolved about the x-axis. Find the volume of the resulting solid.
15. Evaluate the integral.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 7 Form A
16. 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.
17. 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
and the formula
the accompanying table. Use Simpson’s Rule with
to estimate the person’s cardiac output, where D is the quantity of dye injected in milligrams,
is the concentration of the dye in the aorta, and R is measured in liters per minute. Round to one
decimal place.
t
C(t)
0
0
2
0
4
2.6
6
6.3
8
9.7
10
7.5
12
4.5
14
3.5
16
2.2
18. Find a bound on the error in approximating the integral
(b) Simpson’s Rule with
18
0.6
20
0.3
22
0.1
24
0
using (a) the Trapezoidal Rule and
subintervals.
19. A body moves along a coordinate line in such a way that its velocity at any time t, where
is given by
,
.
Find its position function if it is initially located at the origin.
20. Determine whether the improper integral converges or diverges, and if it converges, find its value.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 7 Form A
Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10. divergent
11.
12.
13.
14.
15.
16. a.
5.6884
b.
6.0137
Exact value: 6
17. 6.5 liters per minute
18. a. 3.84, b. 0.98
19.
+ 72
20.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 7 Form B
1. Evaluate the integral.
2. Evaluate the integral.
3. Evaluate the integral.
4. Evaluate the integral.
5. Find the area bounded by the curves
and
between
and
.
6. Evaluate the integral using the indicated trigonometric substitution.
7. Evaluate the integral to six decimal places.
8. Find the volume of the resulting solid if the region under the curve
from
to
is rotated about the x-axis. Round your answer to four decimal places.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 7 Form B
9. Make a substitution to express the integrand as a rational function and then evaluate the integral.
Round the answer to four decimal places.
10. Evaluate the integral.
11. Evaluate the integral.
12. Evaluate the integral.
13. Evaluate the integral.
14. Estimate the area of the shaded region by using the Trapezoidal Rule with
answer to the nearest tenth.
. Round the
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 7 Form B
15. Evaluate the integral or show that it is divergent.
16. Evaluate the integral using an appropriate trigonometric substitution.
17. Find the integral using an appropriate trigonometric substitution.
18. Evaluate the integral.
19. Find the integral.
20. Find a bound on the error in approximating the integral
(b) Simpson’s Rule with
using (a) the Trapezoidal Rule and
subintervals.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 7 Form B
Answer Key
1.
2.
3.
4
15
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14. 8.5
15.
16.
17.
18.
19.
20. a. 3.84, b. 0.98
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 7 Form C
Select the correct answer for each question.
____
1. Evaluate the integral.
a.
b.
c.
d.
e.
____
2. Evaluate the integral using integration by parts with the indicated choices of u and dv.
a.
b.
c.
d.
e.
____
3. Evaluate the integral.
a.
b.
c.
d.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 7 Form C
____
4. Find the integral.
a.
b.
c.
d.
____
5. Evaluate the integral.
a.
b.
c.
d.
e. None of these
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 7 Form C
____
6. Find the average value of the function
in the interval
.
a.
b.
c.
d.
e.
____
7. A particle moves on a straight line with velocity function
. Find its position function
.
a.
b.
c.
d.
e.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 7 Form C
____
8. Use long division to evaluate the integral.
a.
b.
c.
d.
e.
____
9. Find the integral.
a.
b.
c.
d.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 7 Form C
____
10. Find the integral.
a.
b.
c.
d.
____
11. Find the integral.
a.
b.
c.
d.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 7 Form C
____
12. Use a table of integrals to evaluate the integral.
a.
b.
c.
d.
____
13. Use long division to evaluate the integral.
The choices are rounded to 3 decimal places.
a.
b.
c.
d.
e.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 7 Form C
____
14. Evaluate the integral.
a.
b.
c.
d.
e.
____
15. Use a table of integrals to evaluate the integral.
a.
b.
c.
d.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 7 Form C
____
16. Use a table of integrals to evaluate the integral.
a.
b.
c.
d.
____
17. Evaluate the integral or show that it is divergent.
a.
b.
c.
d. 5
4
e.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 7 Form C
____
18. Determine whether the improper integral converges or diverges, and if it converges, find its value.
a. 15
b.

15
2
c. Diverges
d. 15
2
____
19. Let a and b be real numbers. What integral must appear in place of the question mark ”?” to make
the following statement true?
a.
b.
c.
d.
e.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 7 Form C
____
20. Evaluate the integral.
a.
b.
c.
d.
e.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 7 Form C
Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
C
C
A
A
A
B
D
A
A
C
A
A
C
B
B
B
D
B
C
E
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 7 Form D
Select the correct answer for each question.
____
1. Find the integral.
a.
b.
c.
d.
____
2. Evaluate the integral.
a.
b. 6.5700
c. 0.7166
d. 11.8665
e.
____
3. Evaluate the integral using integration by parts with the indicated choices of u and dv.
a.
b.
c.
d.
e.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 7 Form D
____
4. Evaluate the integral.
a.
b.
c.
d.
____
5. Find the integral.
a.
b.
c.
d.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 7 Form D
____
6. Evaluate the integral.
a.
b.
c.
d.
e. None of these
____
7. Evaluate the integral using the indicated trigonometric substitution.
a.
b.
c.
d.
e.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 7 Form D
____
8. Evaluate the integral using an appropriate trigonometric substitution.
a.
b.
c.
d.
____
9. Evaluate the integral.
a.
b.
c.
d.
e.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 7 Form D
____
10. Find the integral.
a.
b.
c.
d.
____
11. Use a table of integrals to evaluate the integral.
a.
b.
c.
d.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 7 Form D
____
12. Use long division to evaluate the integral.
The choices are rounded to 3 decimal places.
a.
b.
c.
d.
e.
____
13. Evaluate the integral.
a.
b.
c.
d.
e.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 7 Form D
____
14. Evaluate the integral.
a.
b.
c.
d.
e.
____
15. Use a table of integrals to evaluate the integral.
a.
b.
c.
d.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 7 Form D
____
16. Use the Trapezoidal Rule to approximate the integral with answers rounded to four decimal places.
a.
b.
c.
d.
____
17. Use Simpson’s Rule to approximate the integral with answers rounded to four decimal places.
a.
b.
c.
d.
____
0.2029
0.1088
0.1163
0.2326
2.0076
2.9504
2.6098
2.2955
18. Find the area bounded by the curves
and
between
and
.
a.
b.
c.
d.
e.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 7 Form D
____
19. The region
is represented below.
Find the area of this region to two decimal places.
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
a. 20.28
b.
c.
d.
e.
____
20. Evaluate the integral.
a.
b.
c.
d.
e.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 7 Form D
Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
D
A
C
A
A
A
D
D
E
C
A
C
D
C
B
A
D
E
A
E
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 7 Form E
____
1. Evaluate the integral. Select the correct answer.
a.
b.
c.
d.
e.
2. Evaluate the indefinite integral.
3. Find the integral.
4. Find the integral.
____
5. Evaluate the integral. Select the correct answer.
a.
b. 6.5700
c. 0.7166
d. 11.8665
e.
6. Evaluate the integral using integration by parts with the indicated choices of u and dv.
7. Evaluate the integral.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 7 Form E
8. Find the integral.
9. Find the average value of the function
____
in the interval
.
10. Find the integral using an appropriate trigonometric substitution. Select the correct answer.
a.
b.
c.
d.
11. Find the integral.
12. Find the integral.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 7 Form E
____
13. Use a table of integrals to evaluate the integral. Select the correct answer.
a.
b.
c.
d.
14. Evaluate the integral.
15. Evaluate the integral.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 7 Form E
____
16. The region under the curve
,
resulting solid. Select the correct answer.
is rotated about the x-axis. Find the volume of the
a.
b. 27
8
c.
d.
e.
17. Use Simpson’s Rule to approximate the integral with answers rounded to four decimal places.
18. Determine whether the improper integral converges or diverges, and if it converges, find its value.
hours but, of course,
19. A manufacturer of light bulbs wants to produce bulbs that last about
some bulbs burn out faster than others. Let
be the fraction of the company's bulbs that burn
out before t hours.
lies between 0 and 1.
Let
. What is the value of
?
20. Evaluate the integral.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 7 Form E
Answer Key
1. C
2.
3.
4.
5. A
6.
7.
8.
9.
10. C
11.
12.
13. B
14.
15.
16. B
17. 2.2955
18.
19.
20.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 7 Form F
____
1. Evaluate the integral. Select the correct answer.
a.
b.
c.
d.
e.
2. Evaluate the integral.
3. Evaluate the integral.
4. Evaluate the integral.
____
5. Find the integral. Select the correct answer.
a.
b.
c.
d.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 7 Form F
6. Evaluate the integral.
7. Evaluate the integral.
8. Find the average value of the function
____
in the interval
.
9. Find the integral using an appropriate trigonometric substitution. Select the correct answer.
a.
b.
c.
d.
10. Find the integral using an appropriate trigonometric substitution.
11. Find the integral.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 7 Form F
____
12. Find the integral. Select the correct answer.
a.
b.
c.
d.
13. Use the Table of Integrals to evaluate the integral.
14. Use a table of integrals to evaluate the integral.
15. Use the Table of Integrals to evaluate the integral.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 7 Form F
____
16. The region under the curve
,
resulting solid. Select the correct answer.
is rotated about the x-axis. Find the volume of the
a.
b. 27
8
c.
d.
e.
17. Use the Trapezoidal Rule to approximate the integral with answers rounded to four decimal places.
18. Use the Midpoint Rule to approximate the given integral with the specified value of n. Compare
your result to the actual value. Find the error in the approximation.
19. Evaluate the integral or show that it is divergent.
20. Determine whether the improper integral converges or diverges, and if it converges, find its value.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 7 Form F
Answer Key
1. C
2.
3.
4.
5. C
6.
7.
8.
9. B
10.
11.
12. A
13.
14.
15.
16. B
17. 0.2029
18. 0.00008
5
19.
4
15
20. 
2
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 7 Form G
1. Evaluate the indefinite integral.
2. Evaluate the integral.
____
3. Find the integral. Select the correct answer.
a.
b.
c.
d.
4. Find the integral.
5. Evaluate the integral.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 7 Form G
____
6. Find the integral. Select the correct answer.
a.
b.
c.
d.
7. Evaluate the integral.
8. Find the integral using an appropriate trigonometric substitution.
9. Use long division to evaluate the integral.
10. Find the integral.
11. Find the integral.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 7 Form G
12. Use long division to evaluate the integral.
The choices are rounded to 3 decimal places.
13. Use the Table of Integrals to evaluate the integral.
14. Use a table of integrals to evaluate the integral.
15. The region under the curve
,
is rotated about the x-axis. Find the volume of the
resulting solid.
____
16. Evaluate the integral or show that it is divergent. Select the correct answer.
a.
b.
c.
d. 5
4
e.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 7 Form G
17. Find the area bounded by the curves
and
between
and
.
18. Determine whether the improper integral converges or diverges, and if it converges, find its value.
19. A manufacturer of light bulbs wants to produce bulbs that last about
hours but, of course,
be the fraction of the company's bulbs that burn
some bulbs burn out faster than others. Let
out before t hours.
lies between 0 and 1.
Let
____
. What is the value of
20. The region
?
is represented below.
Find the area of this region to two decimal places. Select the correct answer.
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
a.
b.
c.
d.
e. 17.93
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart – Calculus ET 8e Chapter 7 Form G
Answer Key
1.
2.
25
2
3. D
4.
5.
6. A
7.
8.
9.
10.
11.
12.
13.
14.
15.
27
2
16. D
17.
15
18. 
2
19.
20. E
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 7 Form H
1. Evaluate the integral.
2. Evaluate the indefinite integral.
3. Find the integral.
____
4. Find the integral. Select the correct answer.
a.
b.
c.
d.
5. Find the average value of the function
in the interval
.
6. Find the integral using an appropriate trigonometric substitution.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 7 Form H
7. Evaluate the integral using the indicated trigonometric substitution.
8. Find the integral using an appropriate trigonometric substitution.
9. Find the integral using an appropriate trigonometric substitution.
____
10. Find the integral. Select the correct answer.
a.
b.
c.
d.
11. Find the integral.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 7 Form H
12. Find the integral.
13. Find the integral.
____
14. Use a table of integrals to evaluate the integral. Select the correct answer.
a.
b.
c.
d.
15. Use the Table of Integrals to evaluate the integral.
16. The region under the curve
,
is rotated about the x-axis. Find the volume of the
resulting solid.
17. Evaluate the integral or show that it is divergent.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 7 Form H
____
18. Determine whether the improper integral converges or diverges, and if it converges, find its value.
Select the correct answer.
a. Diverges
b.
c.
d. 0
19. The region
is represented below.
Find the area of this region to two decimal places.
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
20. Evaluate the integral.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Stewart - Calculus ET 8e Chapter 7 Form H
Answer Key
1.
2.
3.
4. B
5.
6.
7.
8.
9.
10. A
11.
12.
13.
14. D
15.
16.
27
8
5
4
18. C
19. 20.28
17.
20.
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.