Stewart – Calculus 8e ET Chapter 5 Form E
Answer Key
Stewart – Calculus 8e ET Chapter 5 Form F
____ 1. Approximate the area under the curve from using approximating rectangles of
equal widths and right endpoints. The choices are rounded to the nearest hundredth.
Select the correct answer.
a.
b.
c.
d.
e.
____ 2. Evaluate the Riemann sum for with four subintervals, taking the sample
points to be right endpoints. Select the correct answer.
a.
b.
c.
d.
e.
3. Evaluate the integral.
Round your answer to the nearest hundredth.
4. The given expression is the limit of a Riemann sum of a function f on [a, b]. Write this expression
as a definite integral on [a, b].
5. Given that , evaluate the following integral.
Stewart – Calculus 8e ET Chapter 5 Form F
____ 6. Find the area of the region that lies beneath the given curve. Select the correct answer.
,
a. 1.500
b. 1.450
c. –0.500
d. – 1.500
e. 0.500
7. Find the derivative of the function.
____ 8. Evaluate the integral. Select the correct answer.
a. –14
b. –11
c. 10
d. 14
9. Evaluate the integral.
10. Evaluate the limit by interpreting it as the limit of a Riemann sum of a function on the interval
[a, b].
Stewart – Calculus 8e ET Chapter 5 Form F
____ 11. The marginal cost of manufacturing x yards of a certain fabric is
in dollars per yard. Find the increase in cost if the production level is raised from yards to
yards.
Select the correct answer.
a.
b.
c.
d.
e.
12. Evaluate the integral if it exists.
13. Evaluate the integral.
14. Find the indefinite integral.
15. Find the integral.
Stewart – Calculus 8e ET Chapter 5 Form F
____ 16. Find the integral. Select the correct answer.
a.
b.
c.
d.
17. Evaluate the integral.
18. Evaluate the indefinite integral.
19. Find the indefinite integral.
20. Find the integral.
Stewart – Calculus 8e ET Chapter 5 Form F
Answer Key
Stewart – Calculus 8e ET Chapter 5 Form G
____ 1. Use the Midpoint Rule with n = 10 to approximate the integral. Select the correct answer.
a.
b.
c.
d.
e.
2. If where find .
3. Find the area of the region that lies beneath the given curve.
,
4. Find the derivative of the function.
____ 5. Find the general indefinite integral. Select the correct answer.
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 5 Form G
6. Evaluate the integral.
____ 7. Evaluate the integral. Select the correct answer.
a.
b.
c.
d.
e.
8. Evaluate the integral.
9. If
is a child’s rate of growth in pounds per year, which of the following expressions represents
the increase in the child’s weight (in pounds) between the years and ?
10. Evaluate the definite integral.
11. Find the integral using an appropriate trigonometric substitution.
Stewart – Calculus 8e ET Chapter 5 Form G
____ 12. Find the integral. Select the correct answer.
a.
b.
c.
d.
13. Alabama Instruments Company has set up a production line to manufacture a new calculator. The
rate of production of these calculators after t weeks is
calculators per week. Production approaches 5,700 per week as time goes on, but the initial
production is lower because of the workers’ unfamiliarity with the new techniques. Find the
number of calculators produced from the beginning of the third week to the end of the fourth week.
Round the answer to the nearest integer.
14. Evaluate the indefinite integral.
15. Evaluate the integral by making the given substitution.
Stewart – Calculus 8e ET Chapter 5 Form G
____ 16. Evaluate the indefinite integral. Select the correct answer.
a.
b.
c.
d.
e.
17. Find the integral using the indicated substitution.
,
18. Find the indefinite integral.
19. Find the integral.
20. Find the integral.
Stewart – Calculus 8e ET Chapter 5 Form G
Answer Key
Stewart – Calculus 8e ET Chapter 5 Form H
1. Estimate to the hundredth the area from 1 to 5 under the graph of using four
approximating rectangles and right endpoints.
2. Find the area of the region under the graph of f on [a, b].
____ 3. Use the Midpoint Rule with n = 5 to approximate the integral. Select the correct answer.
Round your answer to three decimal places.
a.
b.
c.
d.
e.
____ 4. The given expression is the limit of a Riemann sum of a function f on [a, b]. Write this expression
as a definite integral on [a, b]. Select the correct answer.
a.
b.
c.
d.
Stewart – Calculus 8e ET Chapter 5 Form H
5. Use the following property of the definite integral to estimate the definite integral :
If on [a, b], then
6. Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.
____ 7. Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.
Select the correct answer.
a.
b.
c.
d.
e. none of these
8. Use the following property of the definite integral to estimate the definite integral :
If on [a, b], then
Stewart – Calculus 8e ET Chapter 5 Form H
____ 9. Evaluate the integral. Select the correct answer.
a.
b.
c.
d.
e.
10. Find the general indefinite integral.
11. The marginal cost of manufacturing x yards of a certain fabric is
in dollars per yard. Find the increase in cost if the production level is raised from yards to
yards.
____ 12. Evaluate the integral. Select the correct answer.
a. –0.500
b. –1.000
c.
d. 0.250
e. 1.000
13. Find the indefinite integral.
14. Find the integral.
Stewart – Calculus 8e ET Chapter 5 Form H
____ 15. Alabama Instruments Company has set up a production line to manufacture a new calculator. The
rate of production of these calculators after t weeks is
calculators per week. Production approaches 5,700 per week as time goes on, but the initial
production is lower because of the workers’ unfamiliarity with the new techniques. Find the
number of calculators produced from the beginning of the third week to the end of the fourth week.
Round the answer to the nearest integer.
a.
b.
c.
d.
e.
16. Evaluate the integral by making the given substitution.
17. Evaluate the integral if it exists.
____ 18. Find the indefinite integral. Select the correct answer.
a.
b.
c.
d.
Stewart – Calculus 8e ET Chapter 5 Form H
19. Evaluate the integral.
____ 20. Find the integral using an appropriate trigonometric substitution. Select the correct answer.
a.
b.
c.
d.
Stewart – Calculus 8e ET Chapter 5 Form H
Answer Key