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.
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.
Stewart – Calculus ET 8e Chapter 7 Form F
____ 16. The region under the curve , is rotated about the x-axis. Find the volume of the
resulting solid. Select the correct answer.
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 ET 8e Chapter 7 Form F
Answer Key
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.
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.
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.
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,
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.
246810–2–4–6–8–10 x
2
4
6
8
10
–2
–4
–6
–8
–10
y
a.
b.
c.
d.
e. 17.93
Stewart – Calculus ET 8e Chapter 7 Form G
Answer Key
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.
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.
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.
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.
246810–2–4–6–8–10 x
2
4
6
8
10
–2
–4
–6
–8
–10
y
20. Evaluate the integral.
Stewart – Calculus ET 8e Chapter 7 Form H
Answer Key