Calculus Early Transcendentals 8th Edition by James Stewart - Test Bank

Calculus Early Transcendentals 8th Edition by James Stewart – Test Bank

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Sample Questions Are Posted Below

Stewart – Calculus 8e ET Chapter 5 Form A
© 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.
1. The velocity graph of a braking car is shown. Use it to estimate to the nearest foot the distance
traveled by the car while the brakes are applied. Use a left sum with n = 7.
2. Evaluate by interpreting it in terms of areas.
3. Express the limit as a definite integral on the given interval.
4. Find an expression for the area under the graph of f as a limit. Do not evaluate the limit.
,
5. Find the limit.
6. Find by evaluating the integral using Part 2 of the Fundamental Theorem and then
differentiating.
7. An animal population is increasing at a rate of per year (where t is measured in years).
By how much does the animal population increase between the fourth and tenth years?
Stewart – Calculus 8e ET Chapter 5 Form A
© 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.
8. Evaluate the definite integral.
9. Evaluate the integral.
10. Evaluate the indefinite integral.
11. Use the definition of area to find the area of the region under the graph of f on [a, b] using the
indicated choice of c k.
= , [0, 6], c k is the left endpoint
12. Evaluate the limit after first finding the sum (as a function of n) using the summation formulas.
13. The graph of a function f on the interval [0, 8] is shown in the figure. Compute the Riemann sum
for f on [0, 8] using four subintervals of equal length and choosing the evaluation points to be (a)
the left endpoints, (b) the right endpoints, and (c) the midpoints of the subintervals.
1 2 3 4 5 6 7 8 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
Stewart – Calculus 8e ET Chapter 5 Form A
© 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.
14. You are given function f defined on an interval [a, b], the number n of subintervals of equal length
, and the evaluation points c k in .
(a) Sketch the graph of f and the rectangles associated with the Riemann sum for f on
[a, b], and
(b) find the Riemann sum.
, c k is the right endpoint
15. Evaluate .
16. Let .
a. Use Part 1 of the Fundamental Theorem of Calculus to find .
b. Use Part 2 of the Fundamental Theorem of Calculus to integrate to obtain an
alternative expression for F(x).
c. Differentiate the expression for F(x) found in part (b).
The Fundamental Theorem of Calculus, Part 1
If f is continuous on [a, b], then the function F defined by
is differentiable on (a, b), and
The Fundamental Theorem of Calculus, Part 2
If f is continuous on [a, b], then
where F is any antiderivative of f, that is, .
17. Evaluate the integral.
Stewart – Calculus 8e ET Chapter 5 Form A
© 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.
18. The acceleration function of a body moving along a coordinate line is
.
Find its velocity and position functions at any time t if it is located at the origin and has an initial
velocity of 4 m/sec.
19. Find the indefinite integral.
20. Show that by interpreting the definite integral geometrically.
Stewart – Calculus 8e ET Chapter 5 Form A
© 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.
Answer Key
1. 19
2.
3.
4.
5. 3
6.
7.
8. 0
9.
10.
11. 72
12. 76
3
13. a. 18
b. 10
c. 10
Stewart – Calculus 8e ET Chapter 5 Form A
© 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.
14. a.
1 2 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
b. –1
15. 4
16. a.
b.
c.
17.
18. 7
2 , 7
4
7
4
19.
20. A sketch of the area between the curve and the x-axis, shows that the area below the x-axis is equal
to the area above the x-axis.
 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
Stewart – Calculus 8e ET Chapter 5 Form B
© 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.
1. The speed of a runner increased steadily during the first three seconds of a race. Her speed at
half-second intervals is given in the table. Find a lower estimate for the distance that she traveled
during these three seconds.
2.6 5.2 6.2 8.6 12.7 14.9
2. By reading values from the given graph of , use five rectangles to find a lower estimate, to the
nearest whole number, for the area from 0 to 10 under the given graph of .
3. Approximate the area under the curve from 1 to 2 using ten approximating rectangles of
equal widths and right endpoints. Round the answer to the nearest hundredth.
4. The velocity graph of a braking car is shown. Use it to estimate to the nearest foot the distance
traveled by the car while the brakes are applied. Use a left sum with n = 7.
Stewart – Calculus 8e ET Chapter 5 Form B
© 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.
5. Find an expression for the area under the graph of as a limit. Do not evaluate the limit.
6. If , find the Riemann sum with n = 5 correct to 3 decimal places, taking
the sample points to be midpoints.
7. A table of values of an increasing function is shown. Use the table to find an upper estimate
of:
–41
–34
–23
8
18
30
8. Express the limit as a definite integral on the given interval.
Stewart – Calculus 8e ET Chapter 5 Form B
© 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.
9. Find the area of the region that lies under the given curve.
10. Express the sum as a single integral in the form
.
11. Find an expression for the area under the graph of f as a limit. Do not evaluate the limit.
,
12. The table gives the values of a function obtained from an experiment. Use the values to estimate
using three equal subintervals with left endpoints.
w 0 1 2 3 4 5 6
f (w) 9.7 9.1 7.7 6.1 4.2 –6.6 –10.3
13. Find the limit.
14. Find a function f (x) such that for and some number a.
15. Evaluate the integral.
16. Find the area of the region that lies to the right of the y-axis and to the left of the parabola
.
Stewart – Calculus 8e ET Chapter 5 Form B
© 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.
17. Evaluate the integral.
18. Evaluate the definite integral.
19. Evaluate the integral.
20. Evaluate the integral.
Stewart – Calculus 8e ET Chapter 5 Form B
© 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.
Answer Key
1. 17.65
2. 21
3.
4. 19
5.
6.
7. –210
8.
9. 1
10.
11.
12. 43.2
13. 3
14. ; for 25
64
15.
16. 9
2
17.
18.
19.
20.
Stewart – Calculus 8e ET Chapter 5 Form C
© 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.
Select the correct answer for each question.
____ 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.
a.
b.
c.
d.
e.
____ 2. Evaluate the integral by interpreting it in terms of areas.
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 5 Form C
© 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.
____ 3. Evaluate
a.
b.
c.
d.
e.
____ 4. Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.
a.
b.
c.
d.
e. none of these
Stewart – Calculus 8e ET Chapter 5 Form C
© 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.
____ 5. Find the derivative of the function.
a.
b.  2
9
c.
d.
____ 6. An animal population is increasing at a rate of per year (where t is measured in years).
By how much does the animal population increase between the fourth and tenth years?
a.
b.
c.
d.
e.
____ 7. Evaluate the integral.
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 5 Form C
© 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.
____ 8. The velocity function (in meters per second) is given for a particle moving along a line. Find the
distance traveled by the particle during the given time interval.
a. 36 m
b. 72 m
c. 100 m
d. 64 m
e. 68 m
Stewart – Calculus 8e ET Chapter 5 Form C
© 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.
____ 9. The area of the region that lies to the right of the y-axis and to the left of the parabola
(the shaded region in the figure) is given by the integral .
Find the area..
2 4 6 8–2 x
2
4
6
8
10
–2
y
a.
b.
c.
d. 4
3
e.
Stewart – Calculus 8e ET Chapter 5 Form C
© 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.
____ 10. Find the indefinite integral.
a. 3
7  2 + 5x + C
b.
c. 3
7  2 + 5x + C
d.
____ 11. Evaluate the definite integral.
a.
b. 3.25
c.
d. 0.35
e.
____ 12. Find the indefinite integral.
a. 2x + + C
b. 2x + + C
c. 2x + + C
d. 2x + + C
Stewart – Calculus 8e ET Chapter 5 Form C
© 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.
____ 13. Find the indefinite integral
a.
b.
c.
d.
____ 14. Find the integral.
a.
b.
c.
d.
Stewart – Calculus 8e ET Chapter 5 Form C
© 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.
____ 15. Evaluate the indefinite integral.
a.
b.
c.
d.
e.
____ 16. Evaluate the integral by making the given substitution.
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 5 Form C
© 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.
____ 17. Evaluate the integral.
a.
b.
c.
d.
e. None of these
____ 18. Find the integral.
a.
b.
c.
d.
Stewart – Calculus 8e ET Chapter 5 Form C
© 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.
____ 19. Find the integral using an appropriate trigonometric substitution.
a.
b.
c.
d.
____ 20. Find the integral using an appropriate trigonometric substitution.
a.
b.
c.
d.
Stewart – Calculus 8e ET Chapter 5 Form C
© 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.
Answer Key
1. B
2. A
3. C
4. C
5. D
6. A
7. C
8. E
9. D
10. A
11. A
12. D
13. B
14. A
15. E
16. D
17. D
18. A
19. B
20. C
Stewart – Calculus 8e ET Chapter 5 Form 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.
Select the correct answer for each question.
____ 1. If and , find .
a.
b.
c.
d.
e.
____ 2. Use to evaluate the integral.
a. 18
b. 22
c. 54
d. 22
3
Stewart – Calculus 8e ET Chapter 5 Form 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.
____ 3. 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].
a.
b.
c.
d.
____ 4. Use the following property of the definite integral to estimate the definite integral :
If on [a, b], then
a.
b.
c.
d.
Stewart – Calculus 8e ET Chapter 5 Form 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.
____ 5. Use the following property of the definite integral to estimate the definite integral :
If on [a, b], then
a.
b.
c.
d.
____ 6. Evaluate the integral.
a. –14
b. –11
c. 10
d. 14
____ 7. 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.
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 5 Form 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.
____ 8. The acceleration function (in m/ ) and the initial velocity are given for a particle moving along a
line. Find the velocity at time t and the distance traveled during the given time interval.
a.
b.
c.
d.
e.
____ 9. The velocity of a car was read from its speedometer at ten-second intervals and recorded in the
table. Use the Midpoint Rule to estimate the distance traveled by the car.
0 0 60
10 70
20 80
30 90
40 100
50
a. 1.2 miles
b. 1.8 miles
c. 0.8 miles
d. 2.4 miles
e. 0.6 miles
Stewart – Calculus 8e ET Chapter 5 Form 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.
____ 10. The area of the region that lies to the right of the y-axis and to the left of the parabola
(the shaded region in the figure) is given by the integral .
Find the area..
2 4 6 8–2 x
2
4
6
8
10
–2
y
a.
b.
c.
d. 4
3
e.
Stewart – Calculus 8e ET Chapter 5 Form 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.
____ 11. Find the area of the region under the graph of f on [a, b].
a. 3
b. –12
c. 12
d. –3
Stewart – Calculus 8e ET Chapter 5 Form 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.
____ 12. The area of the region that lies to the right of the y-axis and to the left of the parabola
(the shaded region in the figure) is given by the integral .
Find the area.
a. 6.25
b. 125
c.
d.
e. 45.6
Stewart – Calculus 8e ET Chapter 5 Form 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.
____ 13. Find the indefinite integral.
a. 3
7  7
5 + 4x + C
b.
c. 3
7  7
5 + 4x + C
d.
____ 14. Find the indefinite integral.
a.
b.
c.
d.
Stewart – Calculus 8e ET Chapter 5 Form 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.
____ 15. Evaluate the integral by making the given substitution.
a.
b.
c.
d.
e.
____ 16. Evaluate the indefinite integral.
a.
b.
c.
d.
e.
Stewart – Calculus 8e ET Chapter 5 Form 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.
____ 17. Find the indefinite integral.
a.
b.
c.
d.
____ 18. Evaluate the integral.
a.
b.
c.
d.
e. None of these
Stewart – Calculus 8e ET Chapter 5 Form 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.
____ 19. Find the integral.
a.
b.
c.
d.
____ 20. Find the integral using an appropriate trigonometric substitution.
a.
b.
c.
d.
Stewart – Calculus 8e ET Chapter 5 Form 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.
Answer Key
1. D
2. A
3. D
4. C
5. C
6. C
7. B
8. D
9. A
10. D
11. C
12. D
13. A
14. D
15. D
16. C
17. D
18. D
19. A
20. A
Stewart – Calculus 8e ET Chapter 5 Form 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.
____ 1. Estimate to the hundredth the area from 1 to 5 under the graph of using four
approximating rectangles and right endpoints. Select the correct answer.
a.
b.
c.
d.
e.
f.
2. Determine a region whose area is equal to .
3. Approximate the area under the curve from using approximating rectangles of
equal widths and right endpoints. The choices are rounded to the nearest hundredth.
4. Evaluate the integral by interpreting it in terms of areas.
____ 5. Evaluate the integral. Select the correct answer.
a.
b.
c.
d.
e.
6. Evaluate the integral.
Stewart – Calculus 8e ET Chapter 5 Form 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.
____ 7. Estimate the area from 0 to 5 under the graph of using five approximating
rectangles and right endpoints. Select the correct answer.
a.
b.
c.
d.
e.
8. 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 ?
9. Find the indefinite integral.
____ 10. Evaluate the definite integral. Select the correct answer.
a.
b.
c. 0.35
d. 3.25
e.
11. Find the indefinite integral.
12. Find the integral.
13. Find the integral using an appropriate trigonometric substitution.
Stewart – Calculus 8e ET Chapter 5 Form 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.
14. Find the integral.
____ 15. Evaluate the indefinite integral. Select the correct answer.
a.
b.
c.
d.
e.
16. Find the area of the region that lies under the given curve. Round the answer to three decimal
places.
____ 17. Find the indefinite integral. Select the correct answer.
a.
b. 1
28
c.
d.
18. Find the integral.
Stewart – Calculus 8e ET Chapter 5 Form 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.
19. Find the integral.
____ 20. Find the integral. Select the correct answer.
a.
b.
c.
d.
Stewart – Calculus 8e ET Chapter 5 Form 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.
Answer Key
1. A
2.
3.
4.
5. D
6.
7. A
8.
9. 4
7  7
4 + 8x + C
10. B
11. 1
2  7
4 + 9x + C
12.
13.
14.
15. C
16.
17. B
18.
19.
20. A
Stewart – Calculus 8e ET Chapter 5 Form F
© 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.
____ 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
© 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.
____ 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
© 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.
____ 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
© 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.
____ 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
© 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.
Answer Key
1. B
2. C
3.
4.
5. –5
6. E
7.
8. C
9.
10. 243
5
11. B
12.
13.
14. 3
7  2 + 5x + C
15.
16. C
17.
18.
19.
20.
Stewart – Calculus 8e ET Chapter 5 Form G
© 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.
____ 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
© 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.
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
© 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.
____ 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
© 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.
____ 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
© 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.
Answer Key
1. E
2.
3. 0.500
4.
5. B
6.
7. B
8.
9.
10.
11.
12. C
13.
14.
15.
16. A
17.
18.
19.
20.
Stewart – Calculus 8e ET Chapter 5 Form H
© 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.
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
© 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.
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
© 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.
____ 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
© 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.
____ 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
© 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.
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
© 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.
Answer Key
1.
2. 6
3. D
4. D
5.
6.
7. C
8.
9. A
10.
11.
12. C
13. 3
7  7
5 + 4x + C
14.
15. E
16.
17. none of these
18. D
19.
20. B