Question 1

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.

Accepted Answer

A)  5.3098 
B)  12.2824 
C)  20.6444 
D)  15.9387 
E)  37.9232 
A)  5.3098 
B)  12.2824 
C)  20.6444 
D)  15.9387 
E)  37.9232

Question 2

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.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 3

Find the area of the region bounded by the graphs of the equations.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 4

The figure is the vertical side of a form for poured concrete that weighs 140.7 pounds per cubic foot. Dimensions in the figure are in feet. Determine force on this part of the concrete form

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

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.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 6

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.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line   .

Accepted Answer

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B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 8

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.

Accepted Answer

A)  4681 square feet 
B)  4701 square feet 
C)  2351 square feet 
D)  2000 square feet 
E)  4000 square feet 
A)  4681 square feet 
B)  4701 square feet 
C)  2351 square feet 
D)  2000 square feet 
E)  4000 square feet

Question 9

Find   for the lamina of uniform density   bounded by the graphs of the equations   and   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

Find the area of the region bounded by the graphs of the algebraic functions.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

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 0.01 inches thick.) Round your answer to four decimal places.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 12

A tank on a water tower is a sphere of radius 25 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.

Accepted Answer

A)  16.99 feet 
B)  9.44 feet 
C)  23.91 feet 
D)  16.32 feet 
E)  23.89 feet 
A)  16.99 feet 
B)  9.44 feet 
C)  23.91 feet 
D)  16.32 feet 
E)  23.89 feet

Question 13

A bridge has a main span of about 1350 meters. Each of its towers has a height of about 146 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.

Accepted Answer

A)  695.5 meters 
B)  736.4 meters 
C)  2046.5 meters 
D)  1391 meters 
E)  2782 meters 
A)  695.5 meters 
B)  736.4 meters 
C)  2046.5 meters 
D)  1391 meters 
E)  2782 meters

Question 14

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. ​   ​

Accepted Answer

A)  6.198 m2 
B)  8.883 m2 
C)  6.766 m2 
D)  8.134 m2 
E)  5.267 m2 
A)  6.198 m2 
B)  8.883 m2 
C)  6.766 m2 
D)  8.134 m2 
E)  5.267 m2

Question 15

Find the area of the surface generated by revolving the curve about the x-axis.   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

A circular plate of radius r feet is submerged vertically in a tank of fluid that weighs w pounds per cubic foot. The center of the circle is   feet below the surface of the fluid. The fluid force on the surface of the plate is given by   Find the fluid force on the circular plate as shown in the figure given   feet and   feet and fluid is water. Round your answer to one decimal place.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

An overhead garage door has two springs, one on each side of the door. A force of 16 pounds is required to stretch each spring 1 foot. Because of the pulley system, the springs stretch only one-half the distance the door travels. The door moves a total of 16 feet and springs are at their natural length when the door is open. Find the work done by pair of strings.

Accepted Answer

A)  512 ft-lb 
B)  1,024 ft-lb 
C)  8,192 ft-lb 
D)  4,096 ft-lb 
E)  2,048 ft-lb 
A)  512 ft-lb 
B)  1,024 ft-lb 
C)  8,192 ft-lb 
D)  4,096 ft-lb 
E)  2,048 ft-lb

Question 18

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.

Accepted Answer

A)  9.238 
B)  4.619 
C)  3.893 
D)  15.07 
E)  7.787 
A)  9.238 
B)  4.619 
C)  3.893 
D)  15.07 
E)  7.787

Question 19

Find the center of mass of the given system of point masses.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

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.

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.

Find the area of the region bounded by the graphs of the equations.

The figure is the vertical side of a form for poured concrete that weighs 140.7 pounds per cubic foot. Dimensions in the figure are in feet. Determine force on this part of the concrete form

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.

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.

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line .

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.

Find for the lamina of uniform density bounded by the graphs of the equations and .

Find the area of the region bounded by the graphs of the algebraic functions.

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 0.01 inches thick.) Round your answer to four decimal places.

A tank on a water tower is a sphere of radius 25 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 bridge has a main span of about 1350 meters. Each of its towers has a height of about 146 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.

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.

Find the area of the surface generated by revolving the curve about the x-axis. .

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.

Find the center of mass of the given system of point masses.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Exam 7: Applications of Integration

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.

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.

Find the area of the region bounded by the graphs of the equations.

The figure is the vertical side of a form for poured concrete that weighs 140.7 pounds per cubic foot. Dimensions in the figure are in feet. Determine force on this part of the concrete form

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.

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.

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line .

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.

Find for the lamina of uniform density bounded by the graphs of the equations and . ​

Find the area of the region bounded by the graphs of the algebraic functions.

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 0.01 inches thick.) Round your answer to four decimal places.

A tank on a water tower is a sphere of radius 25 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 bridge has a main span of about 1350 meters. Each of its towers has a height of about 146 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.

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. ​ ​

Find the area of the surface generated by revolving the curve about the x-axis. .

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.

Find the center of mass of the given system of point masses.

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Find for the lamina of uniform density bounded by the graphs of the equations and .

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.