Question 1

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)    D

Question 2

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.

Accepted Answer

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

Question 3

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)    C

Question 4

Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by   axis.

Accepted Answer

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

Question 5

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 6

Set up the definite integral that gives the area of the region bounded by the graph of

Accepted Answer

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

Question 7

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

Accepted Answer

A) 0.260 
B) 0.289 
C) 0.416 
D) 0.139 
E) 0.462 
A) 0.260 
B) 0.289 
C) 0.416 
D) 0.139 
E) 0.462

Question 8

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.

Accepted Answer

A) 20.66 feet 
B) 54.63 feet 
C) 34.67 feet 
D) 42.43 feet 
E) 10.36 feet 
A) 20.66 feet 
B) 54.63 feet 
C) 34.67 feet 
D) 42.43 feet 
E) 10.36 feet

Question 9

If the accumulation function

Accepted Answer

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

Question 10

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) 1.66667 
B) 0.41667 
C) 0.01333 
D) 33.33333 
E) 8.33333 
A) 1.66667 
B) 0.41667 
C) 0.01333 
D) 33.33333 
E) 8.33333

Question 11

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.

Accepted Answer

A) $445.736 billion 
B) $30.221 billion 
C) $7.023 billion 
D) $18.710 billion 
E) $57.880 billion 
A) $445.736 billion 
B) $30.221 billion 
C) $7.023 billion 
D) $18.710 billion 
E) $57.880 billion

Question 12

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 13

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 14

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 15

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 16

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.

Accepted Answer

A) 268,492 pounds 
B) 263,654 pounds 
C) 216,267 pounds 
D) 242,187 pounds 
E) 251,865 pounds 
A) 268,492 pounds 
B) 263,654 pounds 
C) 216,267 pounds 
D) 242,187 pounds 
E) 251,865 pounds

Question 17

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.

Accepted Answer

A) 3.125 
B) 0.160 
C) 0.080 
D) 0.320 
E) 6.250 
A) 3.125 
B) 0.160 
C) 0.080 
D) 0.320 
E) 6.250

Question 18

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 19

Find the area of the region bounded by equations by integrating (i) with respect to   and (ii) with respect to y.

Accepted Answer

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

Question 20

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)

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

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.

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

Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by axis.

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

Set up the definite integral that gives the area of the region bounded by the graph of

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

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.

If the accumulation function

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.

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

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

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

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.

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.

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.

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

Find the area of the region bounded by equations by integrating (i) with respect to and (ii) with respect to y.

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

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Logarithmic, Exponential, and Other Transcendental Functions

Differential Equations

Integration Techniques, Lhôpitals Rule, 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 Analysis

Additional Topics in Differential Equations

Preparation for Calculus

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Exam 7: Applications of Integration

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

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.

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

Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by axis.

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

Set up the definite integral that gives the area of the region bounded by the graph of

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

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.

If the accumulation function

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.

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

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

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

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.

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.

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.

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

Find the area of the region bounded by equations by integrating (i) with respect to and (ii) with respect to y.

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

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Logarithmic, Exponential, and Other Transcendental Functions

Differential Equations

Integration Techniques, Lhôpitals Rule, 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 Analysis

Additional Topics in Differential Equations

Preparation for Calculus

Filters