Stewart – Calculus 8e ET Chapter 5 Form C
____ 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
Answer Key
Stewart – Calculus 8e ET Chapter 5 Form D
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
____ 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
____ 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
____ 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
____ 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..
2468–2 x
2
4
6
8
10
–2
y
a.
b.
c.
d.
4
3
e.
Stewart – Calculus 8e ET Chapter 5 Form D
____ 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
____ 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
____ 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
____ 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
____ 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
____ 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
Answer Key
Stewart – Calculus 8e ET Chapter 5 Form E
____ 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
____ 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
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
19. Find the integral.
____ 20. Find the integral. Select the correct answer.
a.
b.
c.
d.