Question 1

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)    A

Question 2

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.Round your answer to two decimal places. ​

Accepted Answer

A) 192.00 
B) 8.37 
C) 21.30 
D) 66.93 
E) 100.53 
A) 192.00 
B) 8.37 
C) 21.30 
D) 66.93 
E) 100.53 D

Question 3

A bridge has a main span of about 1,200 meters.Each of its towers has a height of about 150 meters.Approximate the length of a parabolic cable along the main span if the length C of the cable is given by   .Round your answer to one decimal place. ​   ​

Accepted Answer

A) 624.1 meters 
B) 671.8 meters 
C) 1,825.7 meters 
D) 1,248.3 meters 
E) 2,496.5 meters 
A) 624.1 meters 
B) 671.8 meters 
C) 1,825.7 meters 
D) 1,248.3 meters 
E) 2,496.5 meters D

Question 4

​A horizontal line   ,where k is greater than 4,is chosen so that the volume of the solid formed when region R is rotated about the line   is twice the volume of the solid found in part (c).Set up,but do not evaluate,an integral expression in terms of a single independent variable which represents the volume of this solid.

Accepted Answer

The answer of ​A horizontal line   ,where k...

Question 5

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 6

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations   ,   ,and   about the line   . ​

Accepted Answer

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

Question 7

A tank on a water tower is a sphere of radius 50 feet.Determine the depth of the water when the tank is filled to one-fourth of its total capacity.(Note: Use the zero or root feature of a graphing utility after evaluating the definite integral. )Round your answer to two decimal places. ​

Accepted Answer

A) 34.72 feet 
B) 12.99 feet 
C) 33.18 feet 
D) 32.64 feet 
E) 28.26 feet 
A) 34.72 feet 
B) 12.99 feet 
C) 33.18 feet 
D) 32.64 feet 
E) 28.26 feet

Question 8

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 9

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 10

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis.Verify your results using the integration capabilities of a graphing utility. ​   ,   ,   ,   ​

Accepted Answer

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

Question 11

Set up and evaluate the definite integral for the area of the surface formed by revolving the graph of   about the y-axis.Round your answer to three decimal places. ​   ​

Accepted Answer

A) 2.665 
B) 5.33 
C) 11.708 
D) 1.294 
E) 0.647 
A) 2.665 
B) 5.33 
C) 11.708 
D) 1.294 
E) 0.647

Question 12

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 13

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 14

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

Accepted Answer

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

Question 15

Electrical wires suspended between two towers form a catenary modeled by the equation   ,   ,where x and y are measured in meters.The towers are 50 meters apart.Find the length of the suspended cable.Round your answer to three decimal places.   ​

Accepted Answer

A) 94.421 m 
B) 50.000 m 
C) 64.077 m 
D) 40.048 m 
E) 47.211 m 
A) 94.421 m 
B) 50.000 m 
C) 64.077 m 
D) 40.048 m 
E) 47.211 m

Question 16

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

Accepted Answer

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

Question 17

A tank on the wing of a jet aircraft is formed by revolving the region bounded by the graph of   and the x-axis   about the x-axis,where x and y are measured in meters.Find the volume of the tank.Round your answer to two decimal places. ​

Accepted Answer

A) 0.37 m3 
B) 0.45 m3 
C) 0.18 m3 
D) 0.68 m3 
E) 0.34 m3 
A) 0.37 m3 
B) 0.45 m3 
C) 0.18 m3 
D) 0.68 m3 
E) 0.34 m3

Question 18

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

Accepted Answer

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

Question 19

Concrete sections for the new building have the dimensions (in meters)and shape as shown in the figure (the picture is not necessarily drawn to scale).Find the area of the face of the section superimposed on the rectangular coordinate system.Round your answer to three decimal places. ​   ​

Accepted Answer

A) 6.198 m2 
B) 8.883 m2 
C) 6.766 m2 
D) 8.134 m2 
E) 5.267 m2 
A) 6.198 m2 
B) 8.883 m2 
C) 6.766 m2 
D) 8.134 m2 
E) 5.267 m2

Question 20

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

Accepted Answer

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

Find the area of the region bounded by the graphs of the algebraic functions.

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.Round your answer to two decimal places.

A bridge has a main span of about 1,200 meters.Each of its towers has a height of about 150 meters.Approximate the length of a parabolic cable along the main span if the length C of the cable is given by .Round your answer to one decimal place.

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

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations , ,and about the line .

A tank on a water tower is a sphere of radius 50 feet.Determine the depth of the water when the tank is filled to one-fourth of its total capacity.(Note: Use the zero or root feature of a graphing utility after evaluating the definite integral. )Round your answer to two decimal places.

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 x-axis. , , ,

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis.Verify your results using the integration capabilities of a graphing utility. , , ,

Set up and evaluate the definite integral for the area of the surface formed by revolving the graph of about the y-axis.Round your answer to three decimal places.

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

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

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

Electrical wires suspended between two towers form a catenary modeled by the equation , ,where x and y are measured in meters.The towers are 50 meters apart.Find the length of the suspended cable.Round your answer to three decimal places.

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

A tank on the wing of a jet aircraft is formed by revolving the region bounded by the graph of and the x-axis about the x-axis,where x and y are measured in meters.Find the volume of the tank.Round your answer to two decimal places.

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

Concrete sections for the new building have the dimensions (in meters)and shape as shown in the figure (the picture is not necessarily drawn to scale).Find the area of the face of the section superimposed on the rectangular coordinate system.Round your answer to three decimal places.

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

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

Find the area of the region bounded by the graphs of the algebraic functions. ​ ​

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.Round your answer to two decimal places. ​

A bridge has a main span of about 1,200 meters.Each of its towers has a height of about 150 meters.Approximate the length of a parabolic cable along the main span if the length C of the cable is given by .Round your answer to one decimal place. ​ ​

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

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations , ,and about the line . ​

A tank on a water tower is a sphere of radius 50 feet.Determine the depth of the water when the tank is filled to one-fourth of its total capacity.(Note: Use the zero or root feature of a graphing utility after evaluating the definite integral. )Round your answer to two decimal places. ​

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 x-axis. ​ , , , ​

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis.Verify your results using the integration capabilities of a graphing utility. ​ , , , ​

Set up and evaluate the definite integral for the area of the surface formed by revolving the graph of about the y-axis.Round your answer to three decimal places. ​ ​

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

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

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

Electrical wires suspended between two towers form a catenary modeled by the equation , ,where x and y are measured in meters.The towers are 50 meters apart.Find the length of the suspended cable.Round your answer to three decimal places. ​

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

A tank on the wing of a jet aircraft is formed by revolving the region bounded by the graph of and the x-axis about the x-axis,where x and y are measured in meters.Find the volume of the tank.Round your answer to two decimal places. ​

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

Concrete sections for the new building have the dimensions (in meters)and shape as shown in the figure (the picture is not necessarily drawn to scale).Find the area of the face of the section superimposed on the rectangular coordinate system.Round your answer to three decimal places. ​ ​

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

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

Find the area of the region bounded by the graphs of the algebraic functions.

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.Round your answer to two decimal places.

A bridge has a main span of about 1,200 meters.Each of its towers has a height of about 150 meters.Approximate the length of a parabolic cable along the main span if the length C of the cable is given by .Round your answer to one decimal place.

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

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations , ,and about the line .

A tank on a water tower is a sphere of radius 50 feet.Determine the depth of the water when the tank is filled to one-fourth of its total capacity.(Note: Use the zero or root feature of a graphing utility after evaluating the definite integral. )Round your answer to two decimal places.

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 x-axis. , , ,

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis.Verify your results using the integration capabilities of a graphing utility. , , ,

Set up and evaluate the definite integral for the area of the surface formed by revolving the graph of about the y-axis.Round your answer to three decimal places.

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

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

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

Electrical wires suspended between two towers form a catenary modeled by the equation , ,where x and y are measured in meters.The towers are 50 meters apart.Find the length of the suspended cable.Round your answer to three decimal places.

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

A tank on the wing of a jet aircraft is formed by revolving the region bounded by the graph of and the x-axis about the x-axis,where x and y are measured in meters.Find the volume of the tank.Round your answer to two decimal places.

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

Concrete sections for the new building have the dimensions (in meters)and shape as shown in the figure (the picture is not necessarily drawn to scale).Find the area of the face of the section superimposed on the rectangular coordinate system.Round your answer to three decimal places.

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