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Exam 7: Applications of Integration

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Exam 1: Preparation for Calculus96 Questionsadd course
Exam 2: Limits and Their Properties119 Questionsadd course
Exam 3: Differentiation208 Questionsadd course
Exam 4: Applications of Differentiation147 Questionsadd course
Exam 5: Integration165 Questionsadd course
Exam 6: Differential Equations88 Questionsadd course
Exam 7: Applications of Integration90 Questionsadd course
Exam 8: Integration Techniques, L'Hôpital's Rule, and Improper Integrals142 Questionsadd course
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Exam 10: Parametric Equations, Polar Coordinates, and Vectors173 Questionsadd course
Exam 11: Mechanical Ventilation and Sedation: Assessment, Medications, and Complications225 Questionsadd course
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Find the volume of the solid generated by revolving the region bounded by the graphs of the equations Find the volume of the solid generated by revolving the region bounded by the graphs of the equations , , ,and about the x-axis.Round your answer to four decimal places. ​ , Find the volume of the solid generated by revolving the region bounded by the graphs of the equations , , ,and about the x-axis.Round your answer to four decimal places. ​ , Find the volume of the solid generated by revolving the region bounded by the graphs of the equations , , ,and about the x-axis.Round your answer to four decimal places. ​ ,and Find the volume of the solid generated by revolving the region bounded by the graphs of the equations , , ,and about the x-axis.Round your answer to four decimal places. ​ about the x-axis.Round your answer to four decimal places. ​

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Question 21

Which of the following expressions represents the volume of the solid generated when the region bounded by Which of the following expressions represents the volume of the solid generated when the region bounded by and is rotated about the line ? ​ and Which of the following expressions represents the volume of the solid generated when the region bounded by and is rotated about the line ? ​ is rotated about the line Which of the following expressions represents the volume of the solid generated when the region bounded by and is rotated about the line ? ​ ? ​

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Question 22

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

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Question 23

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

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Question 24

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 x-axis. ​ 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 x-axis. ​ , , ​ , 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 x-axis. ​ , , ​ , 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 x-axis. ​ , , ​ ​

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Question 25

A solid is generated by revolving the region bounded by A solid is generated by revolving the region bounded by and about the y-axis.A hole,centered along the axis of revolution,is drilled through this solid so that one-third of the volume is removed.Find the diameter of the hole.Round your answer to three decimal places. ​ and A solid is generated by revolving the region bounded by and about the y-axis.A hole,centered along the axis of revolution,is drilled through this solid so that one-third of the volume is removed.Find the diameter of the hole.Round your answer to three decimal places. ​ about the y-axis.A hole,centered along the axis of revolution,is drilled through this solid so that one-third of the volume is removed.Find the diameter of the hole.Round your answer to three decimal places. ​

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Question 26

Use the integration capabilities of a graphing utility to approximate the arc length of the graph of Use the integration capabilities of a graphing utility to approximate the arc length of the graph of on the interval .Round your answer to three decimal places. ​ on the interval Use the integration capabilities of a graphing utility to approximate the arc length of the graph of on the interval .Round your answer to three decimal places. ​ .Round your answer to three decimal places. ​

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Question 27

​Which of the following expressions gives the volume when region R is rotated about the line ​Which of the following expressions gives the volume when region R is rotated about the line ? ​ ? ​

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Question 28

The velocity of a particle moving along a line is given by The velocity of a particle moving along a line is given by for the interval . -​How far to the right of the starting point will the particle be at ? ​ for the interval The velocity of a particle moving along a line is given by for the interval . -​How far to the right of the starting point will the particle be at ? ​ . -​How far to the right of the starting point will the particle be at The velocity of a particle moving along a line is given by for the interval . -​How far to the right of the starting point will the particle be at ? ​ ? ​

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Question 29

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 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 , , ,and about the y-axis.Round your answer to three decimal places. ​ , 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 , , ,and about the y-axis.Round your answer to three decimal places. ​ , 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 , , ,and about the y-axis.Round your answer to three decimal places. ​ ,and 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 , , ,and about the y-axis.Round your answer to three decimal places. ​ about the y-axis.Round your answer to three decimal places. ​

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Question 30

​If the position of the particle at time ​If the position of the particle at time is −1,then what is the position of the particle when it is farthest to the right on this time interval? ​ is −1,then what is the position of the particle when it is farthest to the right on this time interval? ​

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Question 31

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 x-axis. ​ 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 x-axis. ​ , , ​ , 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 x-axis. ​ , , ​ , 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 x-axis. ​ , , ​ ​

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Question 32

A barn is 100 feet long and 40 feet wide.A cross section of the roof is the inverted catenary A barn is 100 feet long and 40 feet wide.A cross section of the roof is the inverted catenary .Find the number of square feet of roofing on the barn.Round your answer to the nearest integer. ​ ​ .Find the number of square feet of roofing on the barn.Round your answer to the nearest integer. ​ A barn is 100 feet long and 40 feet wide.A cross section of the roof is the inverted catenary .Find the number of square feet of roofing on the barn.Round your answer to the nearest integer. ​ ​ ​

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Question 33

Find the area of the region bounded by the graphs of the function Find the area of the region bounded by the graphs of the function , , .Round your answer to three decimal places. ​ , Find the area of the region bounded by the graphs of the function , , .Round your answer to three decimal places. ​ , Find the area of the region bounded by the graphs of the function , , .Round your answer to three decimal places. ​ .Round your answer to three decimal places. ​

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Question 34

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

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Question 35

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

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Question 36

Find the area of the region bounded by equations by integrating (i)with respect to x and (ii)with respect to y. Find the area of the region bounded by equations by integrating (i)with respect to x and (ii)with respect to y. ​ ​ ​ Find the area of the region bounded by equations by integrating (i)with respect to x and (ii)with respect to y. ​ ​ ​

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Question 37

​The revenue and expenditures for a small company are analyzed and predicted for the next 5 years.The current annual revenue is $110,000 and growing at an annual rate of 30%,while the expenditures are modeled with a sinusoidal function.If ​The revenue and expenditures for a small company are analyzed and predicted for the next 5 years.The current annual revenue is $110,000 and growing at an annual rate of 30%,while the expenditures are modeled with a sinusoidal function.If and ,to the nearest dollar,what is the average annual profit for the company when the expenditures reach a maximum value on the interval ? ​ and ​The revenue and expenditures for a small company are analyzed and predicted for the next 5 years.The current annual revenue is $110,000 and growing at an annual rate of 30%,while the expenditures are modeled with a sinusoidal function.If and ,to the nearest dollar,what is the average annual profit for the company when the expenditures reach a maximum value on the interval ? ​ ,to the nearest dollar,what is the average annual profit for the company when the expenditures reach a maximum value on the interval ​The revenue and expenditures for a small company are analyzed and predicted for the next 5 years.The current annual revenue is $110,000 and growing at an annual rate of 30%,while the expenditures are modeled with a sinusoidal function.If and ,to the nearest dollar,what is the average annual profit for the company when the expenditures reach a maximum value on the interval ? ​ ? ​

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Question 38

The chief financial officer of a company reports that profits for the past fiscal year were $17.5 million.The officer predicts that profits for the next 7 years will grow at a continuous annual rate somewhere between The chief financial officer of a company reports that profits for the past fiscal year were $17.5 million.The officer predicts that profits for the next 7 years will grow at a continuous annual rate somewhere between % and 9%.Estimate the cumulative difference in total profit over the 7 years based on the predicted range of growth rates.Round your answer to three decimal places. ​ % and 9%.Estimate the cumulative difference in total profit over the 7 years based on the predicted range of growth rates.Round your answer to three decimal places. ​

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Question 39

Find the area of the region bounded by the equations by integrating (i)with respect to x and (ii)with respect to y. Find the area of the region bounded by the equations by integrating (i)with respect to x and (ii)with respect to y. ​ ​ ​ Find the area of the region bounded by the equations by integrating (i)with respect to x and (ii)with respect to y. ​ ​ ​

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