تكلم مع الذكاء الاصطناعي
Deck 7: Applications of Integration
ملء الشاشة (f)
سؤال
Which of the following expressions gives the volume of a solid whose base in the xy-plane is region Q and whose cross sections,perpendicular to the x-axis,are squares with a side in the xy-plane?
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
In the closed interval 
,if 
,for what value of k does the region bounded by 
and the line 
have the same area as that bounded by 
and the x-axis? 
A)
B)
C)
D)
,if ,for what value of k does the region bounded by and the line have the same area as that bounded by and the x-axis? A)
B)
C)
D)
سؤال
For Question 5,region W is bounded by 
, 
, 
,and 
.
What is the area of the region W?
A)12
B)
C)
D)
, , ,and .
What is the area of the region W?
A)12
B)
C)
D)
سؤال
Air is being pumped into a spherical balloon at the rate of 
cm3/min,but there is a small hole in the balloon and at the same time air is leaking out at the rate of 
cm3/min.
Which of the following is true for
,where t is measured in minutes?
A)
represents the volume of the balloon after the first 10 minutes.
B)
represents the increase in volume each minute during the first 10 minutes.
C)
represents the increase in volume during the first 10 minutes.
D)
cm3/min,but there is a small hole in the balloon and at the same time air is leaking out at the rate of cm3/min.
Which of the following is true for
,where t is measured in minutes?
A)
represents the volume of the balloon after the first 10 minutes.B)
represents the increase in volume each minute during the first 10 minutes.C)
represents the increase in volume during the first 10 minutes.D)
سؤال
Let f be the function given by 
as shown in the sketch below,where the region R is bounded by the graph of 
,the y-axis,and the horizontal line 
.
Find the area of the region R.
as shown in the sketch below,where the region R is bounded by the graph of ,the y-axis,and the horizontal line .
Find the area of the region R.
سؤال
Which of the following expressions gives the volume when region R is rotated about the line 
?
A)
B)
C)
D)
? A)
B)
C)
D)
سؤال
Find the arc length of the graph of the function 
over the interval 
.
A)
B)
C)
D)
E)
over the interval . A)
B)
C)
D)
E)
سؤال
For problems 3 and 4,region Q is bounded by 
, 
, 
and 
.
What is the area of region?
A)0
B)1.5
C)
D)3
, , and .
What is the area of region?
A)0
B)1.5
C)
D)3
سؤال
The velocity of a particle moving along a line is given by 
for the interval 
.
How far to the right of the starting point will the particle be at
?
A)2.212
B)1.548
C)3.318
D)4.424
for the interval .How far to the right of the starting point will the particle be at
? A)2.212
B)1.548
C)3.318
D)4.424
سؤال
The base of a solid is bounded by 
and 
in the xy-plane,as shown in the figure below.Each cross section perpendicular to the x-axis is a rectangle with one side in the xy-plane and whose height is 2.What is the volume of the solid? 
A)3.121
B)4.454
C)6.243
D)12.486
and in the xy-plane,as shown in the figure below.Each cross section perpendicular to the x-axis is a rectangle with one side in the xy-plane and whose height is 2.What is the volume of the solid? A)3.121
B)4.454
C)6.243
D)12.486
سؤال
A horizontal line 
,where k is greater than 4,is chosen so that the volume of the solid formed when region R is rotated about the line 
is twice the volume of the solid found in part (c).Set up,but do not evaluate,an integral expression in terms of a single independent variable which represents the volume of this solid.
,where k is greater than 4,is chosen so that the volume of the solid formed when region R is rotated about the line is twice the volume of the solid found in part (c).Set up,but do not evaluate,an integral expression in terms of a single independent variable which represents the volume of this solid. سؤال
Region G is bounded by the curve 
, 
,and the x-axis.Order from smallest to largest the volumes determined when G is rotated about the axes:
i.
II. 
III. 
A)
B)
C)
D)
, ,and the x-axis.Order from smallest to largest the volumes determined when G is rotated about the axes: i.
II. III. A)
B)
C)
D)
سؤال
If the position of the particle at time 
is −1,then what is the position of the particle when it is farthest to the right on this time interval?
A)2.212
B)6.702
C)13.191
D)10.053
is −1,then what is the position of the particle when it is farthest to the right on this time interval? A)2.212
B)6.702
C)13.191
D)10.053
سؤال
سؤال
Find the combined area of the two regions bounded by the curves 
and 
as shown in the figure bellow. 
A)0.073
B)0.203
C)0.276
D)0.828
and as shown in the figure bellow. A)0.073
B)0.203
C)0.276
D)0.828
سؤال
Find the volume of the solid formed when region R is rotated about the line 
.
. سؤال
Which of the following expressions represents the volume of the solid generated when the region bounded by 
and 
is rotated about the line 
?
A)
B)
C)
D)
and is rotated about the line ? A)
B)
C)
D)
سؤال
A vertical line 
,where 
is chosen so that the area of the region bounded by 
,the y-axis,the horizontal line 
,and the line 
is half the area of region R.What is the value of h?
,where is chosen so that the area of the region bounded by ,the y-axis,the horizontal line ,and the line is half the area of region R.What is the value of h? سؤال
Which of the following expressions gives the area of region R?
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
The revenue and expenditures for a small company are analyzed and predicted for the next 5 years.The current annual revenue is $110,000 and growing at an annual rate of 30%,while the expenditures are modeled with a sinusoidal function.If 
and 
,to the nearest dollar,what is the average annual profit for the company when the expenditures reach a maximum value on the interval 
?
A)191,441
B)159,534
C)119,651
D)79,767
and ,to the nearest dollar,what is the average annual profit for the company when the expenditures reach a maximum value on the interval ? A)191,441
B)159,534
C)119,651
D)79,767
سؤال
Find the arc length of the graph of the function 
over the interval 
.
A)
B)
C)
D)
E)
over the interval . A)
B)
C)
D)
E)
سؤال
Find the area of the surface generated by revolving the curve about the y-axis. 
, 
A)
B)
C)
D)
E)
, A)
B)
C)
D)
E)
سؤال
A bridge has a main span of about 1,200 meters.Each of its towers has a height of about 150 meters.Approximate the length of a parabolic cable along the main span if the length C of the cable is given by 
.Round your answer to one decimal place. 
A)624.1 meters
B)671.8 meters
C)1,825.7 meters
D)1,248.3 meters
E)2,496.5 meters
.Round your answer to one decimal place. A)624.1 meters
B)671.8 meters
C)1,825.7 meters
D)1,248.3 meters
E)2,496.5 meters
سؤال
Use the integration capabilities of a graphing utility to approximate the arc length of the graph of 
on the interval 
.Round your answer to three decimal places.
A)10.340
B)11.740
C)5.270
D)10.540
E)7.640
on the interval .Round your answer to three decimal places. A)10.340
B)11.740
C)5.270
D)10.540
E)7.640
سؤال
Find the arc length of the graph of the function 
over the interval 
.
A)
B)
C)
D)
E)
over the interval . A)
B)
C)
D)
E)
سؤال
Use the shell method to set up and evaluate an integral that gives the volume of the solid generated by revolving the plane region about the y-axis. 
, 
A)
B)
C)
D)
E)
, A)
B)
C)
D)
E)
سؤال
Find the area of the surface generated by revolving the curve about the x-axis. 
, 
A)
B)
C)
D)
E)
, A)
B)
C)
D)
E)
سؤال
Find the area of the surface generated by revolving the curve about the y-axis. 
, 
A)
B)
C)
D)
E)
, A)
B)
C)
D)
E)
سؤال
Find the arc length of the graph of the function 
over the interval 
.
A)
B)
C)
D)
E)
over the interval . A)
B)
C)
D)
E)
سؤال
Electrical wires suspended between two towers form a catenary modeled by the equation 
, 
,where x and y are measured in meters.The towers are 50 meters apart.Find the length of the suspended cable.Round your answer to three decimal places. 
A)94.421 m
B)50.000 m
C)64.077 m
D)40.048 m
E)47.211 m
, ,where x and y are measured in meters.The towers are 50 meters apart.Find the length of the suspended cable.Round your answer to three decimal places. A)94.421 m
B)50.000 m
C)64.077 m
D)40.048 m
E)47.211 m
سؤال
Find the arc length of the graph of the function 
over the interval 
.
A)
B)
C)
D)
E)
over the interval . A)
B)
C)
D)
E)
سؤال
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis. 
, 
, 
A)
B)
C)
D)
E)
, , A)
B)
C)
D)
E)
سؤال
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the arc length of the graph of the function 
over the interval 
.
A)
B)
C)
D)
E)
over the interval . A)
B)
C)
D)
E)
سؤال
Set up and evaluate the definite integral for the area of the surface formed by revolving the graph of 
, 
about the x-axis.
A)
B)
C)
D)
E)
, about the x-axis. A)
B)
C)
D)
E)
سؤال
Set up and evaluate the definite integral for the area of the surface formed by revolving the graph of 
about the y-axis.Round your answer to three decimal places. 
A)2.665
B)5.33
C)11.708
D)1.294
E)0.647
about the y-axis.Round your answer to three decimal places. A)2.665
B)5.33
C)11.708
D)1.294
E)0.647
سؤال
An ornamental light bulb is designed by revolving the graph of 
about the x-axis where x and y are measured in feet.Approximate the amount of glass needed to make the bulb.(Assume that the glass is 0.015 inches thick. )Round your answer to four decimal places. 
A)0.09 in.3
B)0.0006 in.3
C)1.0795 in.3
D)0.0075 in.3
E)5.9971 in.3
about the x-axis where x and y are measured in feet.Approximate the amount of glass needed to make the bulb.(Assume that the glass is 0.015 inches thick. )Round your answer to four decimal places. A)0.09 in.3
B)0.0006 in.3
C)1.0795 in.3
D)0.0075 in.3
E)5.9971 in.3
سؤال
Find the area of the surface generated by revolving the curve about the x-axis. 
, 
A)
B)
C)
D)
E)
, A)
B)
C)
D)
E)
سؤال
A barn is 100 feet long and 40 feet wide.A cross section of the roof is the inverted catenary 
.Find the number of square feet of roofing on the barn.Round your answer to the nearest integer. 
A)4,681 square feet
B)4,701 square feet
C)2,351 square feet
D)2,000 square feet
E)4,000 square feet
.Find the number of square feet of roofing on the barn.Round your answer to the nearest integer. A)4,681 square feet
B)4,701 square feet
C)2,351 square feet
D)2,000 square feet
E)4,000 square feet
سؤال
Find the arc length from 
clockwise to 
along the circle 
.Round your answer to four decimal places.
A)5.4264
B)0.1107
C)0.1137
D)4.3417
E)5.5692
clockwise to along the circle .Round your answer to four decimal places. A)5.4264
B)0.1107
C)0.1137
D)4.3417
E)5.5692
سؤال
Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations 
, 
, 
, 
about the x-axis.Round your answer to two decimal places.
A)192.00
B)8.37
C)21.30
D)66.93
E)100.53
, , , about the x-axis.Round your answer to two decimal places. A)192.00
B)8.37
C)21.30
D)66.93
E)100.53
سؤال
Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations 
, 
, 
about the x-axis.
A)
B)
C)
D)
E)
, , about the x-axis. A)
B)
C)
D)
E)
سؤال
Use the disk or shell method to find the volume of the solid generated by revolving the region in the first quadrant bounded by the graph of the equation about the given line. 
(i)the x-axis; (ii)the y-axis
A)(i)
; (ii)
B)(i)
; (ii)
C)(i)
; (ii)
D)(i)
; (ii)
E)(i)
; (ii)
(i)the x-axis; (ii)the y-axis
A)(i)
; (ii)B)(i)
; (ii)C)(i)
; (ii)D)(i)
; (ii)E)(i)
; (ii) سؤال
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations 
, 
,and 
about the line 
.
A)
B)
C)
D)
E)
, ,and about the line . A)
B)
C)
D)
E)
سؤال
A solid is generated by revolving the region bounded by 
and 
about the y-axis.A hole,centered along the axis of revolution,is drilled through this solid so that one-third of the volume is removed.Find the diameter of the hole.Round your answer to three decimal places.
A)5.774
B)2.887
C)2.433
D)9.419
E)4.867
and about the y-axis.A hole,centered along the axis of revolution,is drilled through this solid so that one-third of the volume is removed.Find the diameter of the hole.Round your answer to three decimal places. A)5.774
B)2.887
C)2.433
D)9.419
E)4.867
سؤال
Use the disk or shell method to 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)
سؤال
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 y-axis.
A)
B)
C)
D)
E)
and in the first quadrant about the y-axis. A)
B)
C)
D)
E)
سؤال
Use the shell method to find the volume of the solid generated by revolving the plane region about the line 
. 
, 
, 
A)
B)
C)
D)
E)
. , , A)
B)
C)
D)
E)
سؤال
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. 
, 
, 
A)
B)
C)
D)
E)
, , A)
B)
C)
D)
E)
سؤال
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. 
, 
, 
A)
B)
C)
D)
E)
, , A)
B)
C)
D)
E)
سؤال
Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by 
, 
,and 
about the y-axis.
A)
B)
C)
D)
E)
, ,and about the y-axis. A)
B)
C)
D)
E)
سؤال
Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by 
and 
about the x-axis.
A)
B)
C)
D)
E)
and about the x-axis. A)
B)
C)
D)
E)
سؤال
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region bounded by 
, 
, 
about the x-axis.
A)
B)
C)
D)
E)
, , about the x-axis. A)
B)
C)
D)
E)
سؤال
A solid is generated by revolving the region bounded by 
and 
about the y-axis.A hole,centered along the axis of revolution,is drilled through this solid so that one-fourth of the volume is removed.Find the diameter of the hole.Round your answer to three decimal places.
A)12.522
B)13.028
C)5.124
D)2.739
E)10.249
and about the y-axis.A hole,centered along the axis of revolution,is drilled through this solid so that one-fourth of the volume is removed.Find the diameter of the hole.Round your answer to three decimal places. A)12.522
B)13.028
C)5.124
D)2.739
E)10.249
سؤال
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region bounded by 
, 
, 
,and 
about the y-axis.Round your answer to three decimal places.
A)3.052
B)0.13
C)1.017
D)0.225
E)0.674
, , ,and about the y-axis.Round your answer to three decimal places. A)3.052
B)0.13
C)1.017
D)0.225
E)0.674
سؤال
Use the disk or shell method to 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)
سؤال
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. 
, 
, 
A)
B)
C)
D)
E)
, , A)
B)
C)
D)
E)
سؤال
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations 
, 
and 
about the line 
.
A)
π
B)
π
C)
D)
E)
π
, and about the line . A)
πB)
πC)
D)
E)
π سؤال
Use the shell method to find the volume of the solid generated by revolving the plane region bounded by 
, 
,about the line 
.
A)
B)
C)
D)
E)
, ,about the line . A)
B)
C)
D)
E)
سؤال
Use the disk or the shell method to 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)
سؤال
Find the area of the region bounded by the graphs of the algebraic functions. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines. 
, 
(i)y-axis; (ii)the line 
A)
; 
B)
; 
C)
; 
D)
; 
E)
; 
, (i)y-axis; (ii)the line A)
; B)
; C)
; D)
; E)
; سؤال
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. 
, 
, 
, 
A)
B)
C)
D)
E)
, , , A)
B)
C)
D)
E)
سؤال
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)
A)
B)
C)
D)
E)
سؤال
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines. 
, 
(i)x-axis; (ii)the line 
A)
; 
B)
; 
C)
; 
D)
; 
E)
; 
, (i)x-axis; (ii)the line A)
; B)
; C)
; D)
; E)
; سؤال
Find the area of the region bounded by the graphs of the algebraic functions. 
, 
, 
, 
A)
B)
C)
D)
E)
, , , A)
B)
C)
D)
E)
سؤال
Find the area of the region bounded by the graphs of the equations. 
, 
, 
A)
B)
C)
D)
E)
, , A)
B)
C)
D)
E)
سؤال
Find the area of the region bounded by the graphs of the algebraic functions. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines. 
, 
(i)x-axis; (ii)the line 
A)(i)
; (ii)
B)(i)
; (ii)
C)(i)
; (ii)
D)(i)
; (ii)
E)(i)
; (ii)
, (i)x-axis; (ii)the line A)(i)
; (ii)B)(i)
; (ii)C)(i)
; (ii)D)(i)
; (ii)E)(i)
; (ii) سؤال
سؤال
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)
سؤال
Set up the definite integral that gives the area of the region bounded by the graph of 
and 
. 
A)
B)
C)
D)
E)
and . A)
B)
C)
D)
E)
سؤال
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis.Verify your results using the integration capabilities of a graphing utility. 
, 
, 
, 
A)
B)
C)
D)
E)
, , , A)
B)
C)
D)
E)
سؤال
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.
A)0.37 m3
B)0.45 m3
C)0.18 m3
D)0.68 m3
E)0.34 m3
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. A)0.37 m3
B)0.45 m3
C)0.18 m3
D)0.68 m3
E)0.34 m3
سؤال
Find the area of the region bounded by the graphs of the algebraic functions. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
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)
سؤال
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations 
, 
, 
,and 
about the x-axis.Round your answer to four decimal places.
A)3.6882
B)10.7186
C)20.6134
D)14.3360
E)37.8922
, , ,and about the x-axis.Round your answer to four decimal places. A)3.6882
B)10.7186
C)20.6134
D)14.3360
E)37.8922
سؤال
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)
سؤال
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)
A)
B)
C)
D)
E)
سؤال
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. 
, 
, 
, 
A)
B)
C)
D)
E)
, , , A)
B)
C)
D)
E)
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العب
ملء الشاشة (f)
Deck 7: Applications of Integration
1
Which of the following expressions gives the volume of a solid whose base in the xy-plane is region Q and whose cross sections,perpendicular to the x-axis,are squares with a side in the xy-plane?
A)
B)
C)
D)
A)
B)
C)
D)
2
In the closed interval ,if ,for what value of k does the region bounded by and the line have the same area as that bounded by and the x-axis?
A)
B)
C)
D)
,if ,for what value of k does the region bounded by and the line have the same area as that bounded by and the x-axis? A)
B)
C)
D)
3
For Question 5,region W is bounded by , , ,and .
What is the area of the region W?
A)12
B)
C)
D)
, , ,and .
What is the area of the region W?
A)12
B)
C)
D)
4
Air is being pumped into a spherical balloon at the rate of cm3/min,but there is a small hole in the balloon and at the same time air is leaking out at the rate of cm3/min.
Which of the following is true for ,where t is measured in minutes?
A) represents the volume of the balloon after the first 10 minutes.
B) represents the increase in volume each minute during the first 10 minutes.
C) represents the increase in volume during the first 10 minutes.
D)
cm3/min,but there is a small hole in the balloon and at the same time air is leaking out at the rate of cm3/min.
Which of the following is true for
,where t is measured in minutes?
A)
represents the volume of the balloon after the first 10 minutes.B)
represents the increase in volume each minute during the first 10 minutes.C)
represents the increase in volume during the first 10 minutes.D)
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5
Let f be the function given by as shown in the sketch below,where the region R is bounded by the graph of ,the y-axis,and the horizontal line .
Find the area of the region R.
as shown in the sketch below,where the region R is bounded by the graph of ,the y-axis,and the horizontal line .
Find the area of the region R.
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6
Which of the following expressions gives the volume when region R is rotated about the line ?
A)
B)
C)
D)
? A)
B)
C)
D)
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7
Find the arc length of the graph of the function over the interval .
A)
B)
C)
D)
E)
over the interval . A)
B)
C)
D)
E)
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8
For problems 3 and 4,region Q is bounded by , , and .
What is the area of region?
A)0
B)1.5
C)
D)3
, , and .
What is the area of region?
A)0
B)1.5
C)
D)3
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9
The velocity of a particle moving along a line is given by for the interval .
How far to the right of the starting point will the particle be at ?
A)2.212
B)1.548
C)3.318
D)4.424
for the interval .How far to the right of the starting point will the particle be at
? A)2.212
B)1.548
C)3.318
D)4.424
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10
The base of a solid is bounded by and in the xy-plane,as shown in the figure below.Each cross section perpendicular to the x-axis is a rectangle with one side in the xy-plane and whose height is 2.What is the volume of the solid?
A)3.121
B)4.454
C)6.243
D)12.486
and in the xy-plane,as shown in the figure below.Each cross section perpendicular to the x-axis is a rectangle with one side in the xy-plane and whose height is 2.What is the volume of the solid? A)3.121
B)4.454
C)6.243
D)12.486
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11
A horizontal line ,where k is greater than 4,is chosen so that the volume of the solid formed when region R is rotated about the line is twice the volume of the solid found in part (c).Set up,but do not evaluate,an integral expression in terms of a single independent variable which represents the volume of this solid.
,where k is greater than 4,is chosen so that the volume of the solid formed when region R is rotated about the line is twice the volume of the solid found in part (c).Set up,but do not evaluate,an integral expression in terms of a single independent variable which represents the volume of this solid. فتح الحزمة
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12
Region G is bounded by the curve , ,and the x-axis.Order from smallest to largest the volumes determined when G is rotated about the axes:
i. II. III.
A)
B)
C)
D)
, ,and the x-axis.Order from smallest to largest the volumes determined when G is rotated about the axes: i.
II. III. A)
B)
C)
D)
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13
If the position of the particle at time is −1,then what is the position of the particle when it is farthest to the right on this time interval?
A)2.212
B)6.702
C)13.191
D)10.053
is −1,then what is the position of the particle when it is farthest to the right on this time interval? A)2.212
B)6.702
C)13.191
D)10.053
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14
What is the distance that the particle has traveled on this time interval?
A)2.212
B)6.596
C)9.234
D)13.191
A)2.212
B)6.596
C)9.234
D)13.191
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15
Find the combined area of the two regions bounded by the curves and as shown in the figure bellow.
A)0.073
B)0.203
C)0.276
D)0.828
and as shown in the figure bellow. A)0.073
B)0.203
C)0.276
D)0.828
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16
Find the volume of the solid formed when region R is rotated about the line .
. فتح الحزمة
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17
Which of the following expressions represents the volume of the solid generated when the region bounded by and is rotated about the line ?
A)
B)
C)
D)
and is rotated about the line ? A)
B)
C)
D)
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18
A vertical line ,where is chosen so that the area of the region bounded by ,the y-axis,the horizontal line ,and the line is half the area of region R.What is the value of h?
,where is chosen so that the area of the region bounded by ,the y-axis,the horizontal line ,and the line is half the area of region R.What is the value of h? فتح الحزمة
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19
Which of the following expressions gives the area of region R?
A)
B)
C)
D)
A)
B)
C)
D)
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20
The revenue and expenditures for a small company are analyzed and predicted for the next 5 years.The current annual revenue is $110,000 and growing at an annual rate of 30%,while the expenditures are modeled with a sinusoidal function.If and ,to the nearest dollar,what is the average annual profit for the company when the expenditures reach a maximum value on the interval ?
A)191,441
B)159,534
C)119,651
D)79,767
and ,to the nearest dollar,what is the average annual profit for the company when the expenditures reach a maximum value on the interval ? A)191,441
B)159,534
C)119,651
D)79,767
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21
Find the arc length of the graph of the function over the interval .
A)
B)
C)
D)
E)
over the interval . A)
B)
C)
D)
E)
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22
Find the area of the surface generated by revolving the curve about the y-axis. ,
A)
B)
C)
D)
E)
, A)
B)
C)
D)
E)
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23
A bridge has a main span of about 1,200 meters.Each of its towers has a height of about 150 meters.Approximate the length of a parabolic cable along the main span if the length C of the cable is given by .Round your answer to one decimal place.
A)624.1 meters
B)671.8 meters
C)1,825.7 meters
D)1,248.3 meters
E)2,496.5 meters
.Round your answer to one decimal place. A)624.1 meters
B)671.8 meters
C)1,825.7 meters
D)1,248.3 meters
E)2,496.5 meters
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24
Use the integration capabilities of a graphing utility to approximate the arc length of the graph of on the interval .Round your answer to three decimal places.
A)10.340
B)11.740
C)5.270
D)10.540
E)7.640
on the interval .Round your answer to three decimal places. A)10.340
B)11.740
C)5.270
D)10.540
E)7.640
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25
Find the arc length of the graph of the function over the interval .
A)
B)
C)
D)
E)
over the interval . A)
B)
C)
D)
E)
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26
Use the shell method to set up and evaluate an integral that gives the volume of the solid generated by revolving the plane region about the y-axis. ,
A)
B)
C)
D)
E)
, A)
B)
C)
D)
E)
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27
Find the area of the surface generated by revolving the curve about the x-axis. ,
A)
B)
C)
D)
E)
, A)
B)
C)
D)
E)
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28
Find the area of the surface generated by revolving the curve about the y-axis. ,
A)
B)
C)
D)
E)
, A)
B)
C)
D)
E)
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29
Find the arc length of the graph of the function over the interval .
A)
B)
C)
D)
E)
over the interval . A)
B)
C)
D)
E)
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30
Electrical wires suspended between two towers form a catenary modeled by the equation , ,where x and y are measured in meters.The towers are 50 meters apart.Find the length of the suspended cable.Round your answer to three decimal places.
A)94.421 m
B)50.000 m
C)64.077 m
D)40.048 m
E)47.211 m
, ,where x and y are measured in meters.The towers are 50 meters apart.Find the length of the suspended cable.Round your answer to three decimal places. A)94.421 m
B)50.000 m
C)64.077 m
D)40.048 m
E)47.211 m
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31
Find the arc length of the graph of the function over the interval .
A)
B)
C)
D)
E)
over the interval . A)
B)
C)
D)
E)
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32
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis. , ,
A)
B)
C)
D)
E)
, , A)
B)
C)
D)
E)
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33
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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34
Find the arc length of the graph of the function over the interval .
A)
B)
C)
D)
E)
over the interval . A)
B)
C)
D)
E)
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35
Set up and evaluate the definite integral for the area of the surface formed by revolving the graph of , about the x-axis.
A)
B)
C)
D)
E)
, about the x-axis. A)
B)
C)
D)
E)
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36
Set up and evaluate the definite integral for the area of the surface formed by revolving the graph of about the y-axis.Round your answer to three decimal places.
A)2.665
B)5.33
C)11.708
D)1.294
E)0.647
about the y-axis.Round your answer to three decimal places. A)2.665
B)5.33
C)11.708
D)1.294
E)0.647
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37
An ornamental light bulb is designed by revolving the graph of about the x-axis where x and y are measured in feet.Approximate the amount of glass needed to make the bulb.(Assume that the glass is 0.015 inches thick. )Round your answer to four decimal places.
A)0.09 in.3
B)0.0006 in.3
C)1.0795 in.3
D)0.0075 in.3
E)5.9971 in.3
about the x-axis where x and y are measured in feet.Approximate the amount of glass needed to make the bulb.(Assume that the glass is 0.015 inches thick. )Round your answer to four decimal places. A)0.09 in.3
B)0.0006 in.3
C)1.0795 in.3
D)0.0075 in.3
E)5.9971 in.3
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38
Find the area of the surface generated by revolving the curve about the x-axis. ,
A)
B)
C)
D)
E)
, A)
B)
C)
D)
E)
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39
A barn is 100 feet long and 40 feet wide.A cross section of the roof is the inverted catenary .Find the number of square feet of roofing on the barn.Round your answer to the nearest integer.
A)4,681 square feet
B)4,701 square feet
C)2,351 square feet
D)2,000 square feet
E)4,000 square feet
.Find the number of square feet of roofing on the barn.Round your answer to the nearest integer. A)4,681 square feet
B)4,701 square feet
C)2,351 square feet
D)2,000 square feet
E)4,000 square feet
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40
Find the arc length from clockwise to along the circle .Round your answer to four decimal places.
A)5.4264
B)0.1107
C)0.1137
D)4.3417
E)5.5692
clockwise to along the circle .Round your answer to four decimal places. A)5.4264
B)0.1107
C)0.1137
D)4.3417
E)5.5692
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41
Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations , , , about the x-axis.Round your answer to two decimal places.
A)192.00
B)8.37
C)21.30
D)66.93
E)100.53
, , , about the x-axis.Round your answer to two decimal places. A)192.00
B)8.37
C)21.30
D)66.93
E)100.53
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42
Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations , , about the x-axis.
A)
B)
C)
D)
E)
, , about the x-axis. A)
B)
C)
D)
E)
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43
Use the disk or shell method to find the volume of the solid generated by revolving the region in the first quadrant bounded by the graph of the equation about the given line.
(i)the x-axis; (ii)the y-axis
A)(i) ; (ii)
B)(i) ; (ii)
C)(i) ; (ii)
D)(i) ; (ii)
E)(i) ; (ii)
(i)the x-axis; (ii)the y-axis
A)(i)
; (ii)B)(i)
; (ii)C)(i)
; (ii)D)(i)
; (ii)E)(i)
; (ii) فتح الحزمة
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44
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations , ,and about the line .
A)
B)
C)
D)
E)
, ,and about the line . A)
B)
C)
D)
E)
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45
A solid is generated by revolving the region bounded by and about the y-axis.A hole,centered along the axis of revolution,is drilled through this solid so that one-third of the volume is removed.Find the diameter of the hole.Round your answer to three decimal places.
A)5.774
B)2.887
C)2.433
D)9.419
E)4.867
and about the y-axis.A hole,centered along the axis of revolution,is drilled through this solid so that one-third of the volume is removed.Find the diameter of the hole.Round your answer to three decimal places. A)5.774
B)2.887
C)2.433
D)9.419
E)4.867
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46
Use the disk or shell method to 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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47
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 y-axis.
A)
B)
C)
D)
E)
and in the first quadrant about the y-axis. A)
B)
C)
D)
E)
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48
Use the shell method to find the volume of the solid generated by revolving the plane region about the line . , ,
A)
B)
C)
D)
E)
. , , A)
B)
C)
D)
E)
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49
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. , ,
A)
B)
C)
D)
E)
, , A)
B)
C)
D)
E)
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50
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. , ,
A)
B)
C)
D)
E)
, , A)
B)
C)
D)
E)
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51
Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by , ,and about the y-axis.
A)
B)
C)
D)
E)
, ,and about the y-axis. A)
B)
C)
D)
E)
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52
Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by and about the x-axis.
A)
B)
C)
D)
E)
and about the x-axis. A)
B)
C)
D)
E)
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53
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region bounded by , , about the x-axis.
A)
B)
C)
D)
E)
, , about the x-axis. A)
B)
C)
D)
E)
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54
A solid is generated by revolving the region bounded by and about the y-axis.A hole,centered along the axis of revolution,is drilled through this solid so that one-fourth of the volume is removed.Find the diameter of the hole.Round your answer to three decimal places.
A)12.522
B)13.028
C)5.124
D)2.739
E)10.249
and about the y-axis.A hole,centered along the axis of revolution,is drilled through this solid so that one-fourth of the volume is removed.Find the diameter of the hole.Round your answer to three decimal places. A)12.522
B)13.028
C)5.124
D)2.739
E)10.249
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55
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region bounded by , , ,and about the y-axis.Round your answer to three decimal places.
A)3.052
B)0.13
C)1.017
D)0.225
E)0.674
, , ,and about the y-axis.Round your answer to three decimal places. A)3.052
B)0.13
C)1.017
D)0.225
E)0.674
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56
Use the disk or shell method to 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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57
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. , ,
A)
B)
C)
D)
E)
, , A)
B)
C)
D)
E)
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58
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations , and about the line .
A) π
B) π
C)
D)
E) π
, and about the line . A)
πB)
πC)
D)
E)
π فتح الحزمة
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59
Use the shell method to find the volume of the solid generated by revolving the plane region bounded by , ,about the line .
A)
B)
C)
D)
E)
, ,about the line . A)
B)
C)
D)
E)
فتح الحزمة
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60
Use the disk or the shell method to 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)
فتح الحزمة
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61
Find the area of the region bounded by the graphs of the algebraic functions.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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62
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines. , (i)y-axis; (ii)the line
A) ;
B) ;
C) ;
D) ;
E) ;
, (i)y-axis; (ii)the line A)
; B)
; C)
; D)
; E)
; فتح الحزمة
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63
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. , , ,
A)
B)
C)
D)
E)
, , , A)
B)
C)
D)
E)
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64
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)
A)
B)
C)
D)
E)
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65
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines. , (i)x-axis; (ii)the line
A) ;
B) ;
C) ;
D) ;
E) ;
, (i)x-axis; (ii)the line A)
; B)
; C)
; D)
; E)
; فتح الحزمة
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66
Find the area of the region bounded by the graphs of the algebraic functions. , , ,
A)
B)
C)
D)
E)
, , , A)
B)
C)
D)
E)
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67
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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68
Find the area of the region bounded by the graphs of the algebraic functions.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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69
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines. , (i)x-axis; (ii)the line
A)(i) ; (ii)
B)(i) ; (ii)
C)(i) ; (ii)
D)(i) ; (ii)
E)(i) ; (ii)
, (i)x-axis; (ii)the line A)(i)
; (ii)B)(i)
; (ii)C)(i)
; (ii)D)(i)
; (ii)E)(i)
; (ii) فتح الحزمة
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70
A tank on a water tower is a sphere of radius 50 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)34.72 feet
B)12.99 feet
C)33.18 feet
D)32.64 feet
E)28.26 feet
A)34.72 feet
B)12.99 feet
C)33.18 feet
D)32.64 feet
E)28.26 feet
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71
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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72
Set up the definite integral that gives the area of the region bounded by the graph of and .
A)
B)
C)
D)
E)
and . A)
B)
C)
D)
E)
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73
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis.Verify your results using the integration capabilities of a graphing utility. , , ,
A)
B)
C)
D)
E)
, , , A)
B)
C)
D)
E)
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74
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.
A)0.37 m3
B)0.45 m3
C)0.18 m3
D)0.68 m3
E)0.34 m3
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. A)0.37 m3
B)0.45 m3
C)0.18 m3
D)0.68 m3
E)0.34 m3
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75
Find the area of the region bounded by the graphs of the algebraic functions.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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76
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)
فتح الحزمة
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77
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations , , ,and about the x-axis.Round your answer to four decimal places.
A)3.6882
B)10.7186
C)20.6134
D)14.3360
E)37.8922
, , ,and about the x-axis.Round your answer to four decimal places. A)3.6882
B)10.7186
C)20.6134
D)14.3360
E)37.8922
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78
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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79
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)
A)
B)
C)
D)
E)
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80
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. , , ,
A)
B)
C)
D)
E)
, , , A)
B)
C)
D)
E)
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