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413 Chapter 7: Applications of Integration
7.1 Area of a Region Between Two Curves
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Set up the definite integral that gives the area of the region bounded by the graph of
and .
a.
b.
c.
d.
e.
____ 2. Find the area of the region bounded by the equations by integrating (i) with respect to x and
(ii) with respect to y.
Area of a Region Between Two Curves
7.1
414
a.
b.
c.
d.
e.
____ 3. Find the area of the region bounded by equations by integrating (i) with respect to x and
(ii) with respect to y.
a.
b.
c.
d.
e.
____ 4. Find the area of the region bounded by the graphs of the algebraic functions.
a.
b.
c.
d.
e.
415 Chapter 7: Applications of Integration
____ 5. Find the area of the region bounded by the graphs of the algebraic functions.
a.
b.
c.
d.
e.
____ 6. Find the area of the region bounded by the graphs of the algebraic functions.
a.
b.
c.
d.
e.
____ 7. Find the area of the region bounded by the graphs of the algebraic functions.
a.
b.
c.
d.
e.
Area of a Region Between Two Curves
7.1
416
____ 8.
Find the area of the region bounded by the graphs of the equations.
a.
b.
c.
d.
e.
____ 9. Find the area of the region bounded by the graphs of the function
. Round your answer to three decimal places.
20.723
11.182
6.238
10.362
22.364
____ 10. Find the area of the region bounded by the graphs of the function
. Round your answer to three decimal places.
0.260
0.289
0.416
0.139
0.462
____ 11. Find the area of the region bounded by the graphs of the equations.
.
a.
b.
c.
d.
e.
417
Chapter 7: Applications of Integration
____
12.
If the accumulation function
is given by
, evaluate
a.
b.
c.
d.
e.
____
13.
Suppose that
and
model the revenue (in billions
of dollars) for a large corporation. The model
gives projected annual revenues from 2008 through
2015, with
corresponding to 2008, and
gives projected revenues if there is a decrease in the
rate of growth of corporate sales over the period. Approximate the total reduction in revenue if
corporate sales are actually closer to the model . Round your answer to three decimal places.
$3.570 billion
$24.990 billion
$19.763 billion
$29.645 billion
$12.495 billion
____ 14.
The chief financial officer of a company reports that profits for the past fiscal year
were $
million. The officer predicts that profits for the next 7 years will grow at a continuous
annual rate somewhere between
% and 6%. Estimate the cumulative difference in total profit over
the 7 years based on the predicted range of growth rates. Round your answer to three decimal places.
$445.736 billion
$30.221 billion
$7.023 billion
$18.710 billion
$57.880 billion
Area of a Region Between Two Curves
7.1
418
____ 15.
The surface of a machine part is the region between the graphs of
and
as shown in the figure. Find k if the parabola is tangent to the graph of . Round
your answer to three decimal places.
3.125
0.160
0.080
0.320
6.250
____ 16. The surface of a machine part is the region between the graphs of and
as shown in the figure. Find the area of the surface of the machine part. Round
your answer to five decimal places.
1.66667
0.41667
0.01333
33.33333
8.33333
419
Chapter 7: Applications of Integration
____
17.
Concrete sections for the new building have the dimensions (in meters) and shape as
shown in the figure (the picture is not necessarily drawn to scale). Find the area of the face of
the section superimposed on the rectangular coordinate system. Round your answer to three
decimal places.
25.031
31.075
29.151
30.515
28.031
____ 18. Concrete sections for the new building have the dimensions (in meters) and shape as
shown in the figure (the picture is not necessarily drawn to scale) . One cubic meter of concrete
weighs 4320 pounds. Find the weight of the section. Round your answer to the nearest pound.
268,492 pounds
263,654 pounds
Area of a Region Between Two Curves
7.1
420
216,267 pounds
242,187 pounds
251,865 pounds
421 Chapter 7: Applications of Integration
7.1 Area of a Region Between Two Curves
Answer Section
7.2 Volume: Disk Method
422
7.2 Volume: The Disk Method
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Set up and evaluate the integral that gives the volume of the solid formed by
revolving the region bounded by and about the -axis.
a.
b.
c.
d.
e.
____ 2.
Set up and evaluate the integral that gives the volume of the solid formed by
revolving the region bounded by
and
in the first quadrant about the -axis.
a.
b.
423 Chapter 7: Applications of Integration
c.
d.
e.
____ 3. Set up and evaluate the integral that gives the volume of the solid formed by revolving the region
bounded by , and about the -axis.
a.
b.
c.
d.
e.
7.2 Volume: Disk Method
424
____ 4.
Find the volume of the solid generated by revolving the region bounded by the
graphs of the equations
, and
about the line
.
448
3
4,480
3
448
3
4,480
3
4,840
3
____ 5.
Find the volume of the solid generated by revolving the region bounded by the
graphs of the equations
, and
about the line
.
a.
16
3
b.
8
3
c.
16
3
d.
32
3
e.
32
3
425 Chapter 7: Applications of Integration
____ 6. Find the volume of the solid generated by revolving the region bounded by the graphs
of the equations about the given lines.
a.
b.
c.
d.
e.
____ 7. Find the volume of the solid generated by revolving the region bounded by the graphs
of the equations about the given lines.
a.
b.
c.
d.
e.
7.2 Volume: Disk Method
426
____ 8. Find the volume of the solid generated by revolving the region bounded by the graphs
of the equations about the given lines.
a.
b.
c.
d.
e.
____ 9.
Find the volume of the solid generated by revolving the region bounded by the
graphs of the equations about the line
.
a.
b.
c.
d.
e.
427 Chapter 7: Applications of Integration
____ 10.
Find the volume of the solid generated by revolving the region bounded by the
graphs of the equations about the line
.
a.
b.
c.
d.
e.
____ 11.
Find the volume of the solid generated by revolving the region bounded by the
graphs of the equations about the line
.
a.
b.
c.
d.
e.
7.2 Volume: Disk Method
428
____ 12.
Find the volume of the solid generated by revolving the region bounded by the
graphs of the equations about the -axis.
a.
b.
c.
d.
e.
____ 13. Find the volume of the solid generated by revolving the region bounded by the
graphs of the equations about the -axis.
a.
b.
c.
d.
e.
429 Chapter 7: Applications of Integration
____ 14. Find the volume of the solid generated by revolving the region bounded by the graphs of
the equations about the -axis. Verify your results using the integration capabilities of a graphing
utility.
a.
b.
c.
d.
e.
____ 15.
Find the volume of the solid generated by revolving the region bounded by the
graphs of the equations
, and
about the -axis. Round your
answer to four decimal places.
5.3098
12.2824
20.6444
15.9387
37.9232
____ 16.
A tank on the wing of a jet aircraft is formed by revolving the region bounded by the
graph of
and the x-axis
about the x-axis, where x and y are measured
in meters. Find the volume of the tank. Round your answer to two decimal places.
0.45 m3
0.33 m3
0.03 m3
1.79 m3
0.12 m3
7.2 Volume: Disk Method
430
____ 17.
A tank on a water tower is a sphere of radius 65 feet. Determine the depth of the
water when the tank is filled to one- fourth of its total capacity. (Note: Use the zero or root feature of
a graphing utility after evaluating the definite integral.) Round your answer to two decimal places.
20.66 feet
54.63 feet
34.67 feet
42.43 feet
10.36 feet
431 Chapter 7: Applications of Integration
7.2 Volume: The Disk Method
Answer Section
7.2 Volume: Disk Method
432
