Question 1

Use the shell method to set up and evaluate the 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)

Question 2

Use the shell method to find the volume of the solid generated by revolving the plane region about the line   . ​   ,   ,   ​

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

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) 3.33333 
B) 0.66667 
C) 0.00333 
D) 166.66667 
E) 33.33333 
A) 3.33333 
B) 0.66667 
C) 0.00333 
D) 166.66667 
E) 33.33333

Question 5

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 x-axis. ​

Accepted Answer

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

Question 6

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 7

​Which of the following expressions gives the volume of a solid whose base in the xy-plane is region Q and whose cross sections,perpendicular to the x-axis,are squares with a side in the xy-plane? ​

Accepted Answer

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

Question 8

Find the arc length from   clockwise to   along the circle   .Round your answer to four decimal places. ​

Accepted Answer

A) 5.4264 
B) 0.1107 
C) 0.1137 
D) 4.3417 
E) 5.5692 
A) 5.4264 
B) 0.1107 
C) 0.1137 
D) 4.3417 
E) 5.5692

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 the integral that gives the volume of the solid generated by revolving the plane region bounded by   ,   ,   about the x-axis. ​

Accepted Answer

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

Question 11

​Find the volume of the solid formed when region R is rotated about the line   .

Accepted Answer

The answer of ​Find the volume of the solid formed...

Question 12

​What is the distance that the particle has traveled on this time interval? ​

Accepted Answer

A) ​2.212 
B) ​6.596 
C) ​9.234 
D) ​13.191 
A) ​2.212 
B) ​6.596 
C) ​9.234 
D) ​13.191

Question 13

If the accumulation function   is given by   ,evaluate   . ​

Accepted Answer

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

Question 14

Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by   ,   ,and   about the y-axis. ​

Accepted Answer

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

Question 15

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 16

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 17

​Which of the following expressions gives the area of region R? ​

Accepted Answer

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

Question 18

Set up and evaluate the definite integral for the area of the surface formed by revolving the graph of   ,   about the x-axis. ​

Accepted Answer

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

Question 19

A vertical line   ,where   is chosen so that the area of the region bounded by   ,the y-axis,the horizontal line   ,and the line   is half the area of region R.What is the value of h?

Accepted Answer

The answer of A vertical line   ,where ...

Question 20

Use the disk or shell method to find the volume of the solid generated by revolving the region in the first quadrant bounded by the graph of the equation about the given line. ​   ​
(i)the x-axis; (ii)the y-axis
​

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)

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

Use the shell method to find the volume of the solid generated by revolving the plane region about the line . , ,

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

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.

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 x-axis.

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 . , ,

Which of the following expressions gives the volume of a solid whose base in the xy-plane is region Q and whose cross sections,perpendicular to the x-axis,are squares with a side in the xy-plane?

Find the arc length from clockwise to along the circle .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 the integral that gives the volume of the solid generated by revolving the plane region bounded by , , about the x-axis.

Find the volume of the solid formed when region R is rotated about the line .

What is the distance that the particle has traveled on this time interval?

If the accumulation function is given by ,evaluate .

Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by , ,and about the y-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 line . , ,

Which of the following expressions gives the area of region R?

Set up and evaluate the definite integral for the area of the surface formed by revolving the graph of , about the x-axis.

A vertical line ,where is chosen so that the area of the region bounded by ,the y-axis,the horizontal line ,and the line is half the area of region R.What is the value of h?

Use the disk or shell method to find the volume of the solid generated by revolving the region in the first quadrant bounded by the graph of the equation about the given line. (i)the x-axis; (ii)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 shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis. ​ , , ​

Use the shell method to find the volume of the solid generated by revolving the plane region about the line . ​ , , ​

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

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. ​ ​

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 x-axis. ​

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 . ​ , , ​

​Which of the following expressions gives the volume of a solid whose base in the xy-plane is region Q and whose cross sections,perpendicular to the x-axis,are squares with a side in the xy-plane? ​

Find the arc length from clockwise to along the circle .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 the integral that gives the volume of the solid generated by revolving the plane region bounded by , , about the x-axis. ​

​Find the volume of the solid formed when region R is rotated about the line .

​What is the distance that the particle has traveled on this time interval? ​

If the accumulation function is given by ,evaluate . ​

Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by , ,and about the y-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 line . ​ , , ​

​Which of the following expressions gives the area of region R? ​

Set up and evaluate the definite integral for the area of the surface formed by revolving the graph of , about the x-axis. ​

A vertical line ,where is chosen so that the area of the region bounded by ,the y-axis,the horizontal line ,and the line is half the area of region R.What is the value of h?

Use the disk or shell method to find the volume of the solid generated by revolving the region in the first quadrant bounded by the graph of the equation about the given line. ​ ​ (i)the x-axis; (ii)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 shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis. , ,

Use the shell method to find the volume of the solid generated by revolving the plane region about the line . , ,

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

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.

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 x-axis.

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 . , ,

Which of the following expressions gives the volume of a solid whose base in the xy-plane is region Q and whose cross sections,perpendicular to the x-axis,are squares with a side in the xy-plane?

Find the arc length from clockwise to along the circle .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 the integral that gives the volume of the solid generated by revolving the plane region bounded by , , about the x-axis.

Find the volume of the solid formed when region R is rotated about the line .

What is the distance that the particle has traveled on this time interval?

If the accumulation function is given by ,evaluate .

Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by , ,and about the y-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 line . , ,

Which of the following expressions gives the area of region R?

Set up and evaluate the definite integral for the area of the surface formed by revolving the graph of , about the x-axis.

Use the disk or shell method to find the volume of the solid generated by revolving the region in the first quadrant bounded by the graph of the equation about the given line. (i)the x-axis; (ii)the y-axis