Question 1

Find the center of mass of the point masses lying on the x-axis.

Accepted Answer

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

Question 2

A cylindrical gasoline tank 4 feet in diameter and 5 feet long is carried on the bank of a truck and is used to fuel tractors. The axis of the tank is horizontal. The opening on the tractor tank is 5 feet above the top of the tank in the truck. Find the work done in pumping the entire gasoline contents that weighs 42 pounds per cubic feet of the fuel tank into a tractor.
(Hint: Evaluate one integral by geometric formula and the other by observing that the integrand is an odd function.

Accepted Answer

A) 11,760 ft-lb 
B) 5,880 ft-lb 
C) 2,940 ft-lb 
D) 31,360 ft-lb 
E) 25,760 ft-lb 
A) 11,760 ft-lb 
B) 5,880 ft-lb 
C) 2,940 ft-lb 
D) 31,360 ft-lb 
E) 25,760 ft-lb B

Question 3

Find the arc length of the graph of the function   over the interval [14, 16].

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

Find the area of the region bounded by the graphs of the function   . Round your answer to three decimal places.

Accepted Answer

A)  36.841 
B)  19.879 
C)  11.090 
D)  18.421 
E)  39.759 
A)  36.841 
B)  19.879 
C)  11.090 
D)  18.421 
E)  39.759

Question 6

Find the fluid force on the vertical side of the tank, where the dimensions are given in feet. Assume that the tank is full of water. Note: The density of water is 62.4 lbs per cubic foot.

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

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.

Accepted Answer

A)  7.440 
B)  8.840 
C)  5.270 
D)  7.640 
E)  3.820 
A)  7.440 
B)  8.840 
C)  5.270 
D)  7.640 
E)  3.820

Question 9

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

Accepted Answer

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

Question 10

A force of 6 pounds compresses a 16-inch spring 4 inches. How much work is done in compressing the spring from a length of 10 inches to a length of 5 inches?

Accepted Answer

A)  68.750000 ft-lb 
B)  65.750000 ft-lb 
C)  63.750000 ft-lb 
D)  58.750000 ft-lb 
E)  73.750000 ft-lb 
A)  68.750000 ft-lb 
B)  65.750000 ft-lb 
C)  63.750000 ft-lb 
D)  58.750000 ft-lb 
E)  73.750000 ft-lb

Question 11

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 12

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.

Accepted Answer

A)  0.09 m3 
B)  0.03 m3 
C)  0.01 m3 
D)  0.17 m3 
E)  0.02 m3 
A)  0.09 m3 
B)  0.03 m3 
C)  0.01 m3 
D)  0.17 m3 
E)  0.02 m3

Question 13

Determine the work done by lifting a 140 pound bag of sugar 7 feet.

Accepted Answer

A)  980 ft-lb 
B)  9,800 ft-lb 
C)  2,100 ft-lb 
D)  98 ft-lb 
E)  210 ft-lb 
A)  980 ft-lb 
B)  9,800 ft-lb 
C)  2,100 ft-lb 
D)  98 ft-lb 
E)  210 ft-lb

Question 14

An open tank has the shape of a right circular cone. The tank is 12 feet across the top and 7 feet high. How much work is done in emptying the tank by pumping the water over the top edge? Note: The density of water is 62.4 lbs per cubic foot.

Accepted Answer

A)  9,172.80   ft-lb 
B)  5,503.68   ft-lb 
C)  7,338.24   ft-lb 
D)  13,759.20   ft-lb 
E)  16,511.04   ft-lb 
A)  9,172.80   ft-lb 
B)  5,503.68   ft-lb 
C)  7,338.24   ft-lb 
D)  13,759.20   ft-lb 
E)  16,511.04   ft-lb

Question 15

Find the fluid force of a triangular vertical plate submerged in water, where the dimensions are given in meters   and the weight-density of water is 9800 newtons per cubic meter.

Accepted Answer

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

Question 16

A rectangular plate of height h feet and base b feet is submerged vertically in a tank of fluid that weighs w pounds per cubic foot. The center of the plate is k 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 rectangular 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

Suppose that   and   model the revenue (in billions of dollars) for a large corporation. The model R1 gives projected annual revenues from 2008 through 2015, with t = 8 corresponding to 2008, and R2 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 R2. Round your answer to three decimal places.

Accepted Answer

A)  $1.540 billion 
B)  $10.780 billion 
C)  $157.780 billion 
D)  $24.010 billion 
E)  $17.710 billion 
A)  $1.540 billion 
B)  $10.780 billion 
C)  $157.780 billion 
D)  $24.010 billion 
E)  $17.710 billion

Question 18

A lunar module weighs 16 tons on the surface of Earth. How much work is done in propelling the module from the surface of the moon to a height of 70 miles? Consider the radius of the moon to be 1100 miles and its force of gravity to be one-sixth that of Earth.

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 19

Find the volume of the solid generated by rotating the circle   about the y-axis.

Accepted Answer

A)  V = 300π2 
B)  V = 60π2 
C)  V = 60π 
D)  V = 300π 
E)  V = 150π2 
A)  V = 300π2 
B)  V = 60π2 
C)  V = 60π 
D)  V = 300π 
E)  V = 150π2

Question 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.

Accepted Answer

A)  4.16667 
B)  2.08333 
C)  0.00213 
D)  104.16667 
E)  52.08333 
A)  4.16667 
B)  2.08333 
C)  0.00213 
D)  104.16667 
E)  52.08333

Find the center of mass of the point masses lying on the x-axis.

Find the arc length of the graph of the function over the interval [14, 16].

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

Find the area of the region bounded by the graphs of the function . Round your answer to three decimal places.

Find the fluid force on the vertical side of the tank, where the dimensions are given in feet. Assume that the tank is full of water. Note: The density of water is 62.4 lbs per cubic foot.

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

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.

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

A force of 6 pounds compresses a 16-inch spring 4 inches. How much work is done in compressing the spring from a length of 10 inches to a length of 5 inches?

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

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.

Determine the work done by lifting a 140 pound bag of sugar 7 feet.

An open tank has the shape of a right circular cone. The tank is 12 feet across the top and 7 feet high. How much work is done in emptying the tank by pumping the water over the top edge? Note: The density of water is 62.4 lbs per cubic foot.

Find the fluid force of a triangular vertical plate submerged in water, where the dimensions are given in meters and the weight-density of water is 9800 newtons per cubic meter.

A lunar module weighs 16 tons on the surface of Earth. How much work is done in propelling the module from the surface of the moon to a height of 70 miles? Consider the radius of the moon to be 1100 miles and its force of gravity to be one-sixth that of Earth.

Find the volume of the solid generated by rotating the circle about the y-axis.

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.

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 center of mass of the point masses lying on the x-axis.

Find the arc length of the graph of the function over the interval [14, 16].

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

Find the area of the region bounded by the graphs of the function . Round your answer to three decimal places.

Find the fluid force on the vertical side of the tank, where the dimensions are given in feet. Assume that the tank is full of water. Note: The density of water is 62.4 lbs per cubic foot.

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

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.

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

A force of 6 pounds compresses a 16-inch spring 4 inches. How much work is done in compressing the spring from a length of 10 inches to a length of 5 inches?

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

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.

Determine the work done by lifting a 140 pound bag of sugar 7 feet.

An open tank has the shape of a right circular cone. The tank is 12 feet across the top and 7 feet high. How much work is done in emptying the tank by pumping the water over the top edge? Note: The density of water is 62.4 lbs per cubic foot.

Find the fluid force of a triangular vertical plate submerged in water, where the dimensions are given in meters and the weight-density of water is 9800 newtons per cubic meter.

A lunar module weighs 16 tons on the surface of Earth. How much work is done in propelling the module from the surface of the moon to a height of 70 miles? Consider the radius of the moon to be 1100 miles and its force of gravity to be one-sixth that of Earth.

Find the volume of the solid generated by rotating the circle about the y-axis.

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.

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