Question 1

Use the disk or the shell method to 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 2

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 3

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)

Question 4

​Find the combined area of the two regions bounded by the curves   and   as shown in the figure bellow. ​   ​

Accepted Answer

A) ​0.073 
B) ​0.203 
C) ​0.276 
D) ​0.828 
A) ​0.073 
B) ​0.203 
C) ​0.276 
D) ​0.828

Question 5

Use the disk or shell method to 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

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines. ​   ,   ​(i)x-axis; (ii)the line   ​

Accepted Answer

A) (i)   ; (ii)
  
B) (i)   ; (ii)
  
C) (i)   ; (ii)
  
D) (i)   ​; (ii)
  
E) (i)   ; (ii)
  
A) (i)   ; (ii)
  
B) (i)   ; (ii)
  
C) (i)   ; (ii)
  
D) (i)   ​; (ii)
  
E) (i)   ; (ii)

Question 7

​In the closed interval   ,if   ,for what value of k does the region bounded by   and the line   have the same area as that bounded by   and the x-axis? ​   ​

Accepted Answer

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

Question 8

An ornamental light bulb is designed by revolving the graph of   about the x-axis where x and y are measured in feet.Approximate the amount of glass needed to make the bulb.(Assume that the glass is 0.015 inches thick. )Round your answer to four decimal places. ​   ​

Accepted Answer

A) 0.09 in.3 
B) 0.0006 in.3 
C) 1.0795 in.3 
D) 0.0075 in.3 
E) 5.9971 in.3 
A) 0.09 in.3 
B) 0.0006 in.3 
C) 1.0795 in.3 
D) 0.0075 in.3 
E) 5.9971 in.3

Question 9

Find the arc length of the graph of the function   over the interval   . ​

Accepted Answer

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

Question 10

Use the shell method to set up and evaluate an integral that gives the volume of the solid generated by revolving the plane region about the y-axis. ​   ,   ​

Accepted Answer

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

Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations , , about the line .

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

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

Find the combined area of the two regions bounded by the curves and as shown in the figure bellow.

Use the disk or shell method to 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 given lines. , (i)x-axis; (ii)the line

In the closed interval ,if ,for what value of k does the region bounded by and the line have the same area as that bounded by and the x-axis?

An ornamental light bulb is designed by revolving the graph of about the x-axis where x and y are measured in feet.Approximate the amount of glass needed to make the bulb.(Assume that the glass is 0.015 inches thick. )Round your answer to four decimal places.

Find the arc length of the graph of the function over the interval .

Use the shell method to set up and evaluate an integral that gives the volume of the solid generated by revolving the plane region about the y-axis. ,

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Exam 7: Applications of Integration

Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations , , about the line . ​

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

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

​Find the combined area of the two regions bounded by the curves and as shown in the figure bellow. ​ ​

Use the disk or shell method to 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 given lines. ​ , ​(i)x-axis; (ii)the line ​

​In the closed interval ,if ,for what value of k does the region bounded by and the line have the same area as that bounded by and the x-axis? ​ ​

An ornamental light bulb is designed by revolving the graph of about the x-axis where x and y are measured in feet.Approximate the amount of glass needed to make the bulb.(Assume that the glass is 0.015 inches thick. )Round your answer to four decimal places. ​ ​

Find the arc length of the graph of the function over the interval . ​

Use the shell method to set up and evaluate an integral that gives the volume of the solid generated by revolving the plane region about the y-axis. ​ , ​

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Integration Techniques, L'Hôpital's Rule, and Improper Integrals

Infinite Series

Parametric Equations, Polar Coordinates, and Vectors

Mechanical Ventilation and Sedation: Assessment, Medications, and Complications

Filters

Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations , , about the line .

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

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

Find the combined area of the two regions bounded by the curves and as shown in the figure bellow.

Use the disk or shell method to 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 given lines. , (i)x-axis; (ii)the line

In the closed interval ,if ,for what value of k does the region bounded by and the line have the same area as that bounded by and the x-axis?

An ornamental light bulb is designed by revolving the graph of about the x-axis where x and y are measured in feet.Approximate the amount of glass needed to make the bulb.(Assume that the glass is 0.015 inches thick. )Round your answer to four decimal places.

Find the arc length of the graph of the function over the interval .

Use the shell method to set up and evaluate an integral that gives the volume of the solid generated by revolving the plane region about the y-axis. ,