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Stewart – Calculus 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.
7. Round the answer to four decimal places.
Use the Table of Integrals to evaluate the integral to three decimal places.Stewart – Calculus 8e Chapter 7 Form A
8. Use the Table of Integrals to evaluate the integral.
9. 10. Use the Trapezoidal Rule to approximate places.
Determine whether the for . Round the result to four decimal
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.Stewart – Calculus 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
the accompanying table. Use Simpson’s Rule with and the formula
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 0 2 4 6 8 10 12 14 16 18 20 22 24
C(t) 0 0 2.6 6.3 9.7 7.5 4.5 3.5 2.2 0.6 0.3 0.1 0
18. using (a) the Trapezoidal Rule and
19. Find a bound on the error in approximating the integral (b) Simpson’s Rule with subintervals.
A body moves along a coordinate line in such a way that its velocity at any time t, where ,
is given by
.
20. Find its position function if it is initially located at the origin.
Determine whether the improper integral converges or diverges, and if it converges, find its value.Stewart – Calculus 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.Stewart – Calculus 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.Stewart – Calculus 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 theStewart – Calculus 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 using (a) the Trapezoidal Rule and
(b) Simpson’s Rule with subintervals.Stewart – Calculus 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. 0.98Stewart – Calculus 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.Stewart – Calculus 8e Chapter 7 Form C
____ 4. Find the integral.
a.
b.
c.
d.
____ 5. Evaluate the integral.
a.
b.
c.
d.
e. None of theseStewart – Calculus 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.Stewart – Calculus 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.Stewart – Calculus 8e Chapter 7 Form C
____ 10. Find the integral.
a.
b.
c.
d.
____ 11. Find the integral.
a.
b.
c.
d.Stewart – Calculus 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.Stewart – Calculus 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.Stewart – Calculus 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.Stewart – Calculus 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.Stewart – Calculus 8e Chapter 7 Form C
____ 20. Evaluate the integral.
a.
b.
c.
d.
e.Stewart – Calculus 8e Chapter 7 Form C
Answer Key
1. C
2. C
3. A
4. A
5. A
6. B
7. D
8. A
9. A
10. C
11. A
12. A
13. C
14. B
15. B
16. B
17. D
18. B
19. C
20. EStewart – Calculus 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.Stewart – Calculus 8e Chapter 7 Form D
____ 4. Evaluate the integral.
a.
b.
c.
d.
____ 5. Find the integral.
a.
b.
c.
d.Stewart – Calculus 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.Stewart – Calculus 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.Stewart – Calculus 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.Stewart – Calculus 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.Stewart – Calculus 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.Stewart – Calculus 8e Chapter 7 Form D
____ 16. Use the Trapezoidal Rule to approximate the integral with answers rounded to four decimal places.
____ 17. a. 0.2029
b. 0.1088
c. 0.1163
d. 0.2326
Use Simpson’s Rule to approximate the integral with answers rounded to four decimal places.
a. 2.0076
b. 2.9504
c. 2.6098
d. 2.2955
____ 18. Find the area bounded by the curves and between and .
a.
b.
c.
d.
e.Stewart – Calculus 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
–8
–6
–4
–2
2 4 6 8 10
–10 x
–2
–4
–6
–8
–10
a. 20.28
b.
c.
d.
e.
____ 20. Evaluate the integral.
a.
b.
c.
d.
e.Stewart – Calculus 8e Chapter 7 Form D
Answer Key
1. D
2. A
3. C
4. A
5. A
6. A
7. D
8. D
9. E
10. C
11. A
12. C
13. D
14. C
15. B
16. A
17. D
18. E
19. A
20. EStewart – Calculus 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.Stewart – Calculus 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.Stewart – Calculus 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.Stewart – Calculus 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.
19. A manufacturer of light bulbs wants to produce bulbs that last about hours but, of course,
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.Stewart – Calculus 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.Stewart – Calculus 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.Stewart – Calculus 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.Stewart – Calculus 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.Stewart – Calculus 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.Stewart – Calculus 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
19. 5
4
20.
15
2Stewart – Calculus 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.Stewart – Calculus 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.Stewart – Calculus 8e Chapter 7 Form G
12. Use long division to evaluate the integral.
13. The choices are rounded to 3 decimal places.
Use the Table of Integrals to evaluate the integral.
14. Use a table of integrals to evaluate the integral.
15. ____ 16. The region under the curve resulting solid.
Evaluate the integral or show that it is divergent. Select the correct answer.
, is rotated about the x-axis. Find the volume of the
a.
b.
c.
d. 5
4
e.Stewart – Calculus 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,
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. 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 x
–8
–6
–4
–2
2 4 6 8 10
–2
–4
–6
–8
–10
a.
b.
c.
d.
e. 17.93Stewart – Calculus 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.
18.
15
2
19.
20. EStewart – Calculus 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.Stewart – Calculus 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.Stewart – Calculus 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. 17. The region under the curve resulting solid.
Evaluate the integral or show that it is divergent.
, is rotated about the x-axis. Find the volume of theStewart – Calculus 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
–8
–6
–4
–2
2 4 6 8 10
–10 x
–2
–4
–6
–8
–10
20. Evaluate the integral.Stewart – Calculus 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
17. 5
4
18. C
19. 20.28
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