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Deck 7: Applications of Integration
Full screen (f)
Question
Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by 
axis.
A)
B)
C)
D)
E)
axis.A)
B)
C)
D)
E)
Question
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
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
Question
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
Round your answer to three decimal places.A)0.260
B)0.289
C)0.416
D)0.139
E)0.462
Question
Suppose that 
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
model the revenue (in billions of dollars) for a large corporation.The model gives projected annual revenues from 2008 through2015, with
corresponding to 2008, and gives projected revenues if there is a decrease in theRate 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
Question
Find the area of the region bounded by the graphs of the algebraic functions. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
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
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
Question
Find the area of the region bounded by equations by integrating (i) with respect to 
and (ii) with respect to y. 
A)
B)
C)
D)
E)
and (ii) with respect to y. A)
B)
C)
D)
E)
Question
Find the area of the region bounded by the graphs of the equations. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the area of the region bounded by the graphs of the algebraic functions. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Set up the definite integral that gives the area of the region bounded by the graph of 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
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)
(ii) with respect to y.
A)
B)
C)
D)
E)
Question
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
million.The officer predicts that profits for the next 7 years will grow at a continuousAnnual rate somewhere between
and 6%.Estimate the cumulative difference in total profit overThe 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
Question
Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by 
in the first quadrant about the -axis.
A)
B)
C)
D)
E)
in the first quadrant about the -axis.A)
B)
C)
D)
E)
Question
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
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
Question
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
Round your answer to three decimal places.A)20.723
B)11.182
C)6.238
D)10.362
E)22.364
Question
If the accumulation function 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the area of the region bounded by the graphs of the algebraic functions. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the area of the region bounded by the graphs of the equations. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the area of the region bounded by the graphs of the algebraic functions. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
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
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
Question
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)
axis. A)
B)
C)
D)
E)
Question
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)
A)
B)
C)
D)
E)
Question
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)
axis. A)
B)
C)
D)
E)
Question
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)
A)
B)
C)
D)
E)
Question
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations 
axis.Round your
Answer to four decimal places.
A)5.3098
B)12.2824
C)20.6444
D)15.9387
E)37.9232
axis.Round yourAnswer to four decimal places.
A)5.3098
B)12.2824
C)20.6444
D)15.9387
E)37.9232
Question
A tank on the wing of a jet aircraft is formed by revolving the region bounded by the graph of 
and the 
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.
A)
B)
C)
D)
E)
and the about the x-axis, where x and y are measured inMeters.Find the volume of the tank.Round your answer to two decimal places.
A)
B)
C)
D)
E)
Question
Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by 
about the -axis.
A)
B)
C)
D)
E)
about the -axis.A)
B)
C)
D)
E)
Question
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)
about the line A)
B)
C)
D)
E)
Question
Question
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)
A)
B)
C)
D)
E)
Question
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)
A)
B)
C)
D)
E)
Question
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)
A)
B)
C)
D)
E)
Question
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)
about the line A)
B)
C)
D)
E)
Question
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)
axis.Verify your results using the integration capabilities of aGraphing utility.
A)
B)
C)
D)
E)
Question
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)
A)
B)
C)
D)
E)
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Deck 7: Applications of Integration
1
Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by axis.
A)
B)
C)
D)
E)
axis.A)
B)
C)
D)
E)
2
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
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
242,187 pounds
3
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
Round your answer to three decimal places.A)0.260
B)0.289
C)0.416
D)0.139
E)0.462
0.260
4
Suppose that 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
model the revenue (in billions of dollars) for a large corporation.The model gives projected annual revenues from 2008 through2015, with
corresponding to 2008, and gives projected revenues if there is a decrease in theRate 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
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5
Find the area of the region bounded by the graphs of the algebraic functions.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
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6
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
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
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
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7
Find the area of the region bounded by equations by integrating (i) with respect to and (ii) with respect to y.
A)
B)
C)
D)
E)
and (ii) with respect to y. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
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8
Find the area of the region bounded by the graphs of the equations.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
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9
Find the area of the region bounded by the graphs of the algebraic functions.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
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10
Set up the definite integral that gives the area of the region bounded by the graph of
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
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11
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)
(ii) with respect to y.
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
k this deck
12
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
million.The officer predicts that profits for the next 7 years will grow at a continuousAnnual rate somewhere between
and 6%.Estimate the cumulative difference in total profit overThe 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
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
k this deck
13
Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by in the first quadrant about the -axis.
A)
B)
C)
D)
E)
in the first quadrant about the -axis.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
k this deck
14
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
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
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
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15
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
Round your answer to three decimal places.A)20.723
B)11.182
C)6.238
D)10.362
E)22.364
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Unlock Deck
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16
If the accumulation function
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
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17
Find the area of the region bounded by the graphs of the algebraic functions.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
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18
Find the area of the region bounded by the graphs of the equations.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
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19
Find the area of the region bounded by the graphs of the algebraic functions.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
k this deck
20
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
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
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
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21
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)
axis. A)
B)
C)
D)
E)
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22
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)
A)
B)
C)
D)
E)
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23
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)
axis. A)
B)
C)
D)
E)
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Unlock for access to all 35 flashcards in this deck.
Unlock Deck
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24
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)
A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
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25
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations axis.Round your
Answer to four decimal places.
A)5.3098
B)12.2824
C)20.6444
D)15.9387
E)37.9232
axis.Round yourAnswer to four decimal places.
A)5.3098
B)12.2824
C)20.6444
D)15.9387
E)37.9232
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
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26
A tank on the wing of a jet aircraft is formed by revolving the region bounded by the graph of and the 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.
A)
B)
C)
D)
E)
and the about the x-axis, where x and y are measured inMeters.Find the volume of the tank.Round your answer to two decimal places.
A)
B)
C)
D)
E)
Unlock Deck
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27
Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by about the -axis.
A)
B)
C)
D)
E)
about the -axis.A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
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28
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)
about the line A)
B)
C)
D)
E)
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29
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.
A)20.66 feet
B)54.63 feet
C)34.67 feet
D)42.43 feet
E)10.36 feet
Graphing utility after evaluating the definite integral.) Round your answer to two decimal places.
A)20.66 feet
B)54.63 feet
C)34.67 feet
D)42.43 feet
E)10.36 feet
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30
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)
A)
B)
C)
D)
E)
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31
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)
A)
B)
C)
D)
E)
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32
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)
A)
B)
C)
D)
E)
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33
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)
about the line A)
B)
C)
D)
E)
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34
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)
axis.Verify your results using the integration capabilities of aGraphing utility.
A)
B)
C)
D)
E)
Unlock Deck
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35
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)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
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