Question 1

Find the integral.

Accepted Answer

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

Question 2

Find the area of the shaded region.

Accepted Answer

A)    
B)    
C)    
D) 7 
A)    
B)    
C)    
D) 7

Question 3

The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method.   about the y-axis

Accepted Answer

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

Question 4

Sketch the region bounded by the graphs of the given equations and find the area of that region. y = sec2 x + 6, y = 8, x = -   , x =

Accepted Answer

A)      - 1 
B)    $\pi$ - 2 
C)    2-$\pi$ 
D)    $\pi$+8 
A)      - 1 
B)    $\pi$ - 2 
C)    2-$\pi$ 
D)    $\pi$+8

Question 5

Find the integral.

Accepted Answer

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

Question 6

Use the method of disks or washers, or the method of cylindrical shells to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated axis. Sketch the region and a representative rectangle.
y = 2x2, y = 4x - 2, y = 8; the y-axis

Accepted Answer

Question 7

Find the area of the region bounded by the given curves.

Accepted Answer

A)    
B)    
C)    
D) 4 
E) 2 
A)    
B)    
C)    
D) 4 
E) 2

Question 8

Use the method of disks or washers, or the method of cylindrical shells to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated axis. Sketch the region and a representative rectangle.   ,   ,   , the x-axis

Accepted Answer

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

Question 9

Suppose you make napkin rings by drilling holes with different diameters through two wooden balls (which also have different diameters). You discover that both napkin rings have the same height h as shown in the figure. Use cylindrical shells to compute the volume of a napkin ring created by drilling a hole with radius d through the center of a sphere of radius D and express the answer in terms of   .

Accepted Answer

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

Question 10

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

Accepted Answer

A)    
B)    
C)    
D)    
E) None of these 
A)    
B)    
C)    
D)    
E) None of these

Question 11

A steel girder weighing 200 lb is hoisted from ground level to the roof of a 40-ft building using a chain that weighs 5 lb/running foot. Find the work done.

Accepted Answer

A) 4,000 ft-lb 
B) 8,100 ft-lb 
C) 12,000 ft-lb 
D) 8,000 ft-lb 
A) 4,000 ft-lb 
B) 8,100 ft-lb 
C) 12,000 ft-lb 
D) 8,000 ft-lb

Question 12

Given that   , evaluate the following integral.

Accepted Answer

A) 5 
B) -5 
C) 20 
D) -20 
A) 5 
B) -5 
C) 20 
D) -20

Question 13

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

Accepted Answer

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

Question 14

The linear density of a   m long rod is   where x is measured in meters from one end of the rod. Find the average density of the rod.

Accepted Answer

The answer of The linear density of a  ...

Question 15

Find the integral using the indicated substitution.   ,

Accepted Answer

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

Question 16

Use a graphing utility to (a) plot the graphs of the given functions, (b) find the approximate x-coordinates of the points of intersection of the graphs, and (c) find an approximation of the volume of the solid obtained by revolving the region bounded by the graphs of the functions about the y-axis. Round answers to two decimal places.
y = x, y = x5 - x2, x $\ge$ 0

Accepted Answer

a. @#IMG-DLM&
b. (0,

Question 17

Find the integral using an appropriate trigonometric substitution.

Accepted Answer

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

Question 18

Find the volume of a cap of a sphere with radius r = 50 and height h =   .

Accepted Answer

The answer of Find the volume of a cap of...

Question 19

Find the area of the shaded region.

Accepted Answer

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

Question 20

Find the area of the region bounded by the parabola   , the tangent line to this parabola at   , and the x axis.

Accepted Answer

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

Find the integral.

Find the area of the shaded region.

The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method. about the y-axis

Sketch the region bounded by the graphs of the given equations and find the area of that region. y = sec² x + 6, y = 8, x = - , x =

Find the integral.

Use the method of disks or washers, or the method of cylindrical shells to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated axis. Sketch the region and a representative rectangle. y = 2x², y = 4x - 2, y = 8; the y-axis

Find the area of the region bounded by the given curves.

Use the method of disks or washers, or the method of cylindrical shells to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated axis. Sketch the region and a representative rectangle. , , , the x-axis

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

A steel girder weighing 200 lb is hoisted from ground level to the roof of a 40-ft building using a chain that weighs 5 lb/running foot. Find the work done.

Given that , evaluate the following integral.

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

The linear density of a m long rod is where x is measured in meters from one end of the rod. Find the average density of the rod.

Find the integral using the indicated substitution. ,

Find the integral using an appropriate trigonometric substitution.

Find the volume of a cap of a sphere with radius r = 50 and height h = .

Find the area of the shaded region.

Find the area of the region bounded by the parabola , the tangent line to this parabola at , and the x axis.

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

Exam 5: Applications of Integration

Find the integral.

Find the area of the shaded region.

The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method. about the y-axis

Sketch the region bounded by the graphs of the given equations and find the area of that region. y = sec2 x + 6, y = 8, x = - , x =

Find the integral.

Use the method of disks or washers, or the method of cylindrical shells to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated axis. Sketch the region and a representative rectangle. y = 2x2, y = 4x - 2, y = 8; the y-axis

Find the area of the region bounded by the given curves.

Use the method of disks or washers, or the method of cylindrical shells to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated axis. Sketch the region and a representative rectangle. , , , the x-axis

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

A steel girder weighing 200 lb is hoisted from ground level to the roof of a 40-ft building using a chain that weighs 5 lb/running foot. Find the work done.

Given that , evaluate the following integral.

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

The linear density of a m long rod is where x is measured in meters from one end of the rod. Find the average density of the rod.

Find the integral using the indicated substitution. ,

Find the integral using an appropriate trigonometric substitution.

Find the volume of a cap of a sphere with radius r = 50 and height h = .

Find the area of the shaded region.

Find the area of the region bounded by the parabola , the tangent line to this parabola at , and the x axis.

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

Sketch the region bounded by the graphs of the given equations and find the area of that region. y = sec² x + 6, y = 8, x = - , x =

Use the method of disks or washers, or the method of cylindrical shells to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated axis. Sketch the region and a representative rectangle. y = 2x², y = 4x - 2, y = 8; the y-axis