Question 1

The Mean Value Theorem for Integrals says that if   is continuous on [   ,   ], then there exists a number m in [   ,   ] such that   .

Accepted Answer

A) True 
 B)False  False

Question 2

Evaluate the integral.

Accepted Answer

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

Question 3

Find the volume of the solid obtained by rotating the region bounded by   and   about the y-axis.

Accepted Answer

The answer of Find the volume of the solid obtained...

Question 4

Use the Midpoint Rule with n =   to approximate the area of the region bounded by the given curves.

Accepted Answer

The answer of Use the Midpoint Rule with n =...

Question 5

A heavy rope,   ft long, weighs   lb/ft and hangs over the edge of a building 110 ft high. How much work is done in pulling the rope to the top of the building?

Accepted Answer

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

Question 6

Find the volume of the solid that is obtained by revolving the region about the line y =   .

Accepted Answer

A) 89$\pi$ 
B)     $\pi$ 
C)    $\pi$ 
D)    $\pi$ 
A) 89$\pi$ 
B)     $\pi$ 
C)    $\pi$ 
D)    $\pi$

Question 7

Find the average value of the function   on the interval   .

Accepted Answer

The answer of Find the average value of the function...

Question 8

Find the indefinite integral

Accepted Answer

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

Question 9

Find the integral using an appropriate trigonometric substitution.

Accepted Answer

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

Question 10

Find the integral using the indicated substitution.   ,

Accepted Answer

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

Question 11

A tank has the shape of an inverted right circular cone with a base radius of 4 m and a height of 9 m. If the tank is filled to a height of 3 m, find the work required (to the nearest joule) to empty the tank by pumping the water over the top of the tank. (The mass of water is 1000 kg/m3 and the force of gravity is 9.8 m/sec2.)

Accepted Answer

Question 12

Sketch the region enclosed by   . Find the area of the region.

Accepted Answer

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

Question 13

Find the integral using an appropriate trigonometric substitution.

Accepted Answer

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

Question 14

Find the volume of the solid obtained by rotating about the x-axis the region under the curve   from x =   to x =   .

Accepted Answer

The answer of Find the volume of the solid obtained...

Question 15

Use the following property of the definite integral to estimate the definite integral   : If   on [a, b], then

Accepted Answer

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

Question 16

Find the indefinite integral

Accepted Answer

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

Question 17

Find the number(s) a such that the average value of the function   on the interval   is equal to 10.

Accepted Answer

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

Question 18

Sketch a plane region and indicate the axis about which it is revolved so that the resulting solid of revolution (found using the shell method) is given by the integral. 2$\pi$

Accepted Answer

A)    y-axis 
B)    y-axis 
C)    x-axis 
D)    x-axis 
A)    y-axis 
B)    y-axis 
C)    x-axis 
D)    x-axis

Question 19

Find the average value of the function   on the interval   . Round your answer to 3 decimal places.

Accepted Answer

A) 0.45 
B) 9.342 
C)    
D) 0.432 
E) 18 
A) 0.45 
B) 9.342 
C)    
D) 0.432 
E) 18

Question 20

Find the average value of the function   on the interval   .

Accepted Answer

The answer of Find the average value of the function...

The Mean Value Theorem for Integrals says that if is continuous on [ , ], then there exists a number m in [ , ] such that .

Evaluate the integral.

Find the volume of the solid obtained by rotating the region bounded by and about the y-axis.

Use the Midpoint Rule with n = to approximate the area of the region bounded by the given curves.

A heavy rope, ft long, weighs lb/ft and hangs over the edge of a building 110 ft high. How much work is done in pulling the rope to the top of the building?

Find the volume of the solid that is obtained by revolving the region about the line y = .

Find the average value of the function on the interval .

Find the indefinite integral

Find the integral using an appropriate trigonometric substitution.

Find the integral using the indicated substitution. ,

Sketch the region enclosed by . Find the area of the region.

Find the integral using an appropriate trigonometric substitution.

Find the volume of the solid obtained by rotating about the x-axis the region under the curve from x = to x = .

Use the following property of the definite integral to estimate the definite integral : If on [a, b], then

Find the indefinite integral

Find the number(s) a such that the average value of the function on the interval is equal to 10.

Find the average value of the function on the interval . Round your answer to 3 decimal places.

Find the average value of the function on the interval .

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

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Exam 5: Applications of Integration

The Mean Value Theorem for Integrals says that if is continuous on [ , ], then there exists a number m in [ , ] such that .

Evaluate the integral.

Find the volume of the solid obtained by rotating the region bounded by and about the y-axis.

Use the Midpoint Rule with n = to approximate the area of the region bounded by the given curves.

A heavy rope, ft long, weighs lb/ft and hangs over the edge of a building 110 ft high. How much work is done in pulling the rope to the top of the building?

Find the volume of the solid that is obtained by revolving the region about the line y = .

Find the average value of the function on the interval .

Find the indefinite integral

Find the integral using an appropriate trigonometric substitution.

Find the integral using the indicated substitution. ,

Sketch the region enclosed by . Find the area of the region.

Find the integral using an appropriate trigonometric substitution.

Find the volume of the solid obtained by rotating about the x-axis the region under the curve from x = to x = .

Use the following property of the definite integral to estimate the definite integral : If on [a, b], then

Find the indefinite integral

Find the number(s) a such that the average value of the function on the interval is equal to 10.

Sketch a plane region and indicate the axis about which it is revolved so that the resulting solid of revolution (found using the shell method) is given by the integral. 2 π\piπ

Find the average value of the function on the interval . Round your answer to 3 decimal places.

Find the average value of the function on the interval .

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters