390 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.
7.1 Area of a Region Between Two Curves 391
____ 2. Find the area of the region bounded by the equations by integrating (i) with respect to
x and
(ii) with respect to y.
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.
392 Chapter 7: Applications of Integration
d.
e.
____ 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.
7.1 Area of a Region Between Two Curves 393
c.
d.
e.
____ 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.
a. 20.723
b. 11.182
c. 6.238
d. 10.362
e. 22.364
____ 10. Find the area of the region bounded by the graphs of the function
. Round your answer to three decimal places.
a. 0.260
b. 0.289
c. 0.416
d. 0.139
e. 0.462
____ 11. Find the area of the region bounded by the graphs of the equations.
.
a.
b.
c.
394 Chapter 7: Applications of Integration
d.
e.
____ 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.
a. $3.570 billion
b. $24.990 billion
c. $19.763 billion
d. $29.645 billion
e. $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.
a. $445.736 billion
b. $30.221 billion
c. $7.023 billion
d. $18.710 billion
e. $57.880 billion
7.1 Area of a Region Between Two Curves 395
____ 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.
a. 3.125
b. 0.160
c. 0.080
d. 0.320
e. 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.
a. 1.66667
b. 0.41667
c. 0.01333
d. 33.33333
e. 8.33333
396 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.
a. 25.031
b. 31.075
c. 29.151
d. 30.515
e. 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.
a. 268,492 pounds
b. 263,654 pounds
c. 216,267 pounds
d. 242,187 pounds
e. 251,865 pounds
7.1 Area of a Region Between Two Curves 397
7.1 Area of a Region Between Two Curves
Answer Section