Question 1

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 2

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 3

A force of 25 pounds stretches a spring 11 inches in an exercise machine. Find the work done in stretching the spring 3 feet from its natural position. ​

Accepted Answer

A)    ft-lb 
B)    ft-lb 
C)    ft-lb 
D)    ft-lb 
E)    ft-lb 
A)    ft-lb 
B)    ft-lb 
C)    ft-lb 
D)    ft-lb 
E)    ft-lb

Question 4

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   .

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 bounded by   about the y-axis. Round your answer to three decimal places.

Accepted Answer

A)  6.529 
B)  0.533 
C)  2.42 
D)  0.923 
E)  2.769 
A)  6.529 
B)  0.533 
C)  2.42 
D)  0.923 
E)  2.769

Question 6

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 7

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.

Accepted Answer

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

Question 8

A tank with a base of 4 feet by 5 feet and a height of 4 feet is full of water. The water weighs 62.4 pounds per cubic foot. How much work is done in pumping water out over the top edge in order to empty all of the tank. Round your answer to one decimal place.

Accepted Answer

A)  1,996.8 ft-lb 
B)  1,248.0 ft-lb 
C)  2,496.0 ft-lb 
D)  499.2 ft-lb 
E)  9,984.0 ft-lb 
A)  1,996.8 ft-lb 
B)  1,248.0 ft-lb 
C)  2,496.0 ft-lb 
D)  499.2 ft-lb 
E)  9,984.0 ft-lb

Question 9

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.

Accepted Answer

A)  1.789 
B)  1.861 
C)  0.732 
D)  1.035 
E)  1.464 
A)  1.789 
B)  1.861 
C)  0.732 
D)  1.035 
E)  1.464

Question 10

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 11

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 y1. Round your answer to three decimal places.

Accepted Answer

A)  6.250 
B)  0.080 
C)  0.040 
D)  0.160 
E)  12.500 
A)  6.250 
B)  0.080 
C)  0.040 
D)  0.160 
E)  12.500

Question 12

A quantity of a gas with an initial volume of 2 cubic feet and a pressure of 4500 pounds per square foot expands to a volume of 7 cubic feet. Find the work done by the gas. Round your answer to two decimal places. Assume the temperature of the gas in this process remain constant.

Accepted Answer

A)  5,637.43 ft-lb 
B)  11,274.87 ft-lb 
C)  3,214.29 ft-lb 
D)  2,066.33 ft-lb 
E)  14,484.94 ft-lb 
A)  5,637.43 ft-lb 
B)  11,274.87 ft-lb 
C)  3,214.29 ft-lb 
D)  2,066.33 ft-lb 
E)  14,484.94 ft-lb

Question 13

Find Mx, My, and   for the lamina of uniform density ρ bounded by the graphs of the equations   .

Accepted Answer

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

Question 14

Neglecting air resistance and the weight of the propellant, determine the work done in propelling a 10-ton satellite to a height of 200 miles above Earth. Assume that the Earth has a radius of 4000 miles.

Accepted Answer

A)  2,857.14 mi-ton 
B)  1,904.76 mi-ton 
C)  1,142.86 mi-ton 
D)  1,523.81 mi-ton 
E)  4,190.48 mi-ton 
A)  2,857.14 mi-ton 
B)  1,904.76 mi-ton 
C)  1,142.86 mi-ton 
D)  1,523.81 mi-ton 
E)  4,190.48 mi-ton

Question 15

Find the arc length from   clockwise to   along the circle   . Round your answer to four decimal places.

Accepted Answer

A)  2.5232 
B)  0.2804 
C)  0.2432 
D)  1.764 
E)  2.1892 
A)  2.5232 
B)  0.2804 
C)  0.2432 
D)  1.764 
E)  2.1892

Question 16

Find the arc length of the graph of the function   over the interval [1,2].

Accepted Answer

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

Question 17

Find the arc length of the graph of the function   over the interval [0,5].

Accepted Answer

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

Question 18

The area of the top side of a piece of sheet metal is 10 square feet. The sheet metal is submerged horizontally in 6 feet of water. Find the fluid force on the top side. Round your answer to one decimal place.

Accepted Answer

A)  3,744.0 lb 
B)  3,684.0 lb 
C)  3,624.0 lb 
D)  3,852.0 lb 
E)  4,032.0 lb 
A)  3,744.0 lb 
B)  3,684.0 lb 
C)  3,624.0 lb 
D)  3,852.0 lb 
E)  4,032.0 lb

Question 19

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 20

A cylindrical water tank 5 meters high with a radius of 3 meters is buried so that the top of the tank is 1 meter below ground level. How much work is done in pumping a full tank of water up to ground level? (The water weighs 9800 newtons per cubic meter.)

Accepted Answer

A)  1,234,800   joules 
B)  1,543,500   joules 
C)  926,100   joules 
D)  2,778,300   joules 
E)  2,315,250   joules 
A)  1,234,800   joules 
B)  1,543,500   joules 
C)  926,100   joules 
D)  2,778,300   joules 
E)  2,315,250   joules

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

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 force of 25 pounds stretches a spring 11 inches in an exercise machine. Find the work done in stretching the spring 3 feet from its natural position.

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 .

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 y-axis. Round your answer to three decimal places.

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

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 tank with a base of 4 feet by 5 feet and a height of 4 feet is full of water. The water weighs 62.4 pounds per cubic foot. How much work is done in pumping water out over the top edge in order to empty all of the tank. Round your answer to one decimal place.

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.

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.

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 y₁. Round your answer to three decimal places.

A quantity of a gas with an initial volume of 2 cubic feet and a pressure of 4500 pounds per square foot expands to a volume of 7 cubic feet. Find the work done by the gas. Round your answer to two decimal places. Assume the temperature of the gas in this process remain constant.

Find M_x, M_y, and for the lamina of uniform density ρ bounded by the graphs of the equations .

Neglecting air resistance and the weight of the propellant, determine the work done in propelling a 10-ton satellite to a height of 200 miles above Earth. Assume that the Earth has a radius of 4000 miles.

Find the arc length from clockwise to along the circle . Round your answer to four decimal places.

Find the arc length of the graph of the function over the interval [1,2].

Find the arc length of the graph of the function over the interval [0,5].

The area of the top side of a piece of sheet metal is 10 square feet. The sheet metal is submerged horizontally in 6 feet of water. Find the fluid force on the top side. Round your answer to one decimal place.

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 cylindrical water tank 5 meters high with a radius of 3 meters is buried so that the top of the tank is 1 meter below ground level. How much work is done in pumping a full tank of water up to ground level? (The water weighs 9800 newtons per cubic meter.)

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

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 force of 25 pounds stretches a spring 11 inches in an exercise machine. Find the work done in stretching the spring 3 feet from its natural position. ​

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 .

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 y-axis. Round your answer to three decimal places.

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

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 tank with a base of 4 feet by 5 feet and a height of 4 feet is full of water. The water weighs 62.4 pounds per cubic foot. How much work is done in pumping water out over the top edge in order to empty all of the tank. Round your answer to one decimal place.

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.

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.

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 y1. Round your answer to three decimal places.

A quantity of a gas with an initial volume of 2 cubic feet and a pressure of 4500 pounds per square foot expands to a volume of 7 cubic feet. Find the work done by the gas. Round your answer to two decimal places. Assume the temperature of the gas in this process remain constant.

Find Mx, My, and for the lamina of uniform density ρ bounded by the graphs of the equations .

Neglecting air resistance and the weight of the propellant, determine the work done in propelling a 10-ton satellite to a height of 200 miles above Earth. Assume that the Earth has a radius of 4000 miles.

Find the arc length from clockwise to along the circle . Round your answer to four decimal places.

Find the arc length of the graph of the function over the interval [1,2].

Find the arc length of the graph of the function over the interval [0,5].

The area of the top side of a piece of sheet metal is 10 square feet. The sheet metal is submerged horizontally in 6 feet of water. Find the fluid force on the top side. Round your answer to one decimal place.

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 cylindrical water tank 5 meters high with a radius of 3 meters is buried so that the top of the tank is 1 meter below ground level. How much work is done in pumping a full tank of water up to ground level? (The water weighs 9800 newtons per cubic meter.)

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

A force of 25 pounds stretches a spring 11 inches in an exercise machine. Find the work done in stretching the spring 3 feet from its natural position.

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 y₁. Round your answer to three decimal places.

Find M_x, M_y, and for the lamina of uniform density ρ bounded by the graphs of the equations .