Question 1

Find the indefinite integral.

Accepted Answer

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

Question 2

Use the method of cylindrical shells to find the volume of the solid generated by revolving the region about the indicated axis or line.   y-axis

Accepted Answer

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

Question 3

Use   to evaluate the integral.

Accepted Answer

A) 22 
B)    
C)    
D) 54 
A) 22 
B)    
C)    
D) 54

Question 4

Use the method of cylindrical shells to find the volume of solid obtained by rotating the region bounded by the given curves about the x axis.

Accepted Answer

The answer of Use the method of cylindrical shells to...

Question 5

Evaluate the integral

Accepted Answer

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

Question 6

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line. y = 1 - x2, y = 0; the line y = 4

Accepted Answer

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

Question 7

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y = sin x + 1, x = 0, y = 0, x = $\pi$

Accepted Answer

A)    $\pi$2 +2$\pi$ 
B) $\pi$2+2$\pi$ 
C)    $\pi$2+4$\pi$ 
D) $\pi$2+4$\pi$ 
A)    $\pi$2 +2$\pi$ 
B) $\pi$2+2$\pi$ 
C)    $\pi$2+4$\pi$ 
D) $\pi$2+4$\pi$

Question 8

Find the area of the region bounded by the given curves (a) using integration with respect to x and (b) using integration with respect to y.
y = 2x3, y = 5x + 6, x = 0

Accepted Answer

Question 9

A force of 30 N is required to maintain a spring stretched from its natural length of 12 cm to a length of 15 cm. How much work is done in stretching the spring from   cm to   cm?

Accepted Answer

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

Question 10

A chain weighing 3 lb/ft hangs vertically from a winch located 13 ft above the ground, and the free end of the chain is just touching the ground. Find the work done by the winch in pulling in the whole chain.

Accepted Answer

The answer of A chain weighing 3 lb/ft hangs vertically...

Question 11

Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

Accepted Answer

The answer of Set up, but do not evaluate, an...

Question 12

Use 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 =   , y = -x + 5; the y-axis

Accepted Answer

A) 250$\pi$  
B)    $\pi$
  
C)    $\pi$
  
D) 250$\pi$
  
A) 250$\pi$  
B)    $\pi$
  
C)    $\pi$
  
D) 250$\pi$

Question 13

Find the work done in pushing a car a distance of   m while exerting a constant force of   N.

Accepted Answer

The answer of Find the work done in pushing a...

Question 14

Find the indefinite integral.

Accepted Answer

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

Question 15

An aquarium   m long,   m wide, and 1 m deep is full of water. Find the work (in J) needed to pump half of the water out of the aquarium. (Use the facts that the density of water is   and   )

Accepted Answer

The answer of An aquarium   m long, ...

Question 16

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

Accepted Answer

The answer of Sketch the region enclosed by  ...

Question 17

Find the indefinite integral.

Accepted Answer

A) 2x +       + C 
B) 2x +       + C 
C) 2x +       + C 
D) 2x +       + C 
A) 2x +       + C 
B) 2x +       + C 
C) 2x +       + C 
D) 2x +       + C

Question 18

Find the integral.

Accepted Answer

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

Question 19

Find the average value of the function   on the interval   .

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 indicated line. Sketch the region and a representative rectangle.
y =   , y = x - 1; the line x = 2

Accepted Answer

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

Find the indefinite integral.

Use the method of cylindrical shells to find the volume of the solid generated by revolving the region about the indicated axis or line. y-axis

Use to evaluate the integral.

Use the method of cylindrical shells to find the volume of solid obtained by rotating the region bounded by the given curves about the x axis.

Evaluate the integral

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line. y = 1 - x², y = 0; the line y = 4

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y = sin x + 1, x = 0, y = 0, x = $\pi$

Find the area of the region bounded by the given curves (a) using integration with respect to x and (b) using integration with respect to y. y = 2x³, y = 5x + 6, x = 0

A force of 30 N is required to maintain a spring stretched from its natural length of 12 cm to a length of 15 cm. How much work is done in stretching the spring from cm to cm?

A chain weighing 3 lb/ft hangs vertically from a winch located 13 ft above the ground, and the free end of the chain is just touching the ground. Find the work done by the winch in pulling in the whole chain.

Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

Use 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 = , y = -x + 5; the y-axis

Find the work done in pushing a car a distance of m while exerting a constant force of N.

Find the indefinite integral.

An aquarium m long, m wide, and 1 m deep is full of water. Find the work (in J) needed to pump half of the water out of the aquarium. (Use the facts that the density of water is and )

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

Find the indefinite integral.

Find the integral.

Find the average value of the function on the interval .

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line. Sketch the region and a representative rectangle. y = , y = x - 1; the line x = 2

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 indefinite integral.

Use the method of cylindrical shells to find the volume of the solid generated by revolving the region about the indicated axis or line. y-axis

Use to evaluate the integral.

Use the method of cylindrical shells to find the volume of solid obtained by rotating the region bounded by the given curves about the x axis.

Evaluate the integral

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line. y = 1 - x2, y = 0; the line y = 4

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y = sin x + 1, x = 0, y = 0, x = π\piπ

Find the area of the region bounded by the given curves (a) using integration with respect to x and (b) using integration with respect to y. y = 2x3, y = 5x + 6, x = 0

A force of 30 N is required to maintain a spring stretched from its natural length of 12 cm to a length of 15 cm. How much work is done in stretching the spring from cm to cm?

A chain weighing 3 lb/ft hangs vertically from a winch located 13 ft above the ground, and the free end of the chain is just touching the ground. Find the work done by the winch in pulling in the whole chain.

Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

Use 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 = , y = -x + 5; the y-axis

Find the work done in pushing a car a distance of m while exerting a constant force of N.

Find the indefinite integral.

An aquarium m long, m wide, and 1 m deep is full of water. Find the work (in J) needed to pump half of the water out of the aquarium. (Use the facts that the density of water is and )

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

Find the indefinite integral.

Find the integral.

Find the average value of the function on the interval .

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line. Sketch the region and a representative rectangle. y = , y = x - 1; the line x = 2

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

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line. y = 1 - x², y = 0; the line y = 4

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y = sin x + 1, x = 0, y = 0, x = $\pi$

Find the area of the region bounded by the given curves (a) using integration with respect to x and (b) using integration with respect to y. y = 2x³, y = 5x + 6, x = 0