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Set up a triple integral for the volume of the solid bounded by the coordinate planes and the plane given below. Set up a triple integral for the volume of the solid bounded by the coordinate planes and the plane given below. A) B) C) D) E)


A) Set up a triple integral for the volume of the solid bounded by the coordinate planes and the plane given below. A) B) C) D) E)
B) Set up a triple integral for the volume of the solid bounded by the coordinate planes and the plane given below. A) B) C) D) E)
C) Set up a triple integral for the volume of the solid bounded by the coordinate planes and the plane given below. A) B) C) D) E)
D) Set up a triple integral for the volume of the solid bounded by the coordinate planes and the plane given below. A) B) C) D) E)
E) Set up a triple integral for the volume of the solid bounded by the coordinate planes and the plane given below. A) B) C) D) E)

F) A) and E)
G) A) and C)

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Find the area of the portion of the surface Find the area of the portion of the surface that lies above the region . Round your answer to two decimal places. A) 29.20 B) 58.39 C) 439.36 D) 36.18 E) 1.64 that lies above the region Find the area of the portion of the surface that lies above the region . Round your answer to two decimal places. A) 29.20 B) 58.39 C) 439.36 D) 36.18 E) 1.64 . Round your answer to two decimal places.


A) 29.20
B) 58.39
C) 439.36
D) 36.18
E) 1.64

F) A) and B)
G) C) and D)

Correct Answer

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Rewrite the iterated integral Rewrite the iterated integral using the order dydxdz. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​ using the order dydxdz. ​ ​


A) ​ Rewrite the iterated integral using the order dydxdz. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​
B) ​ Rewrite the iterated integral using the order dydxdz. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​
C) ​ Rewrite the iterated integral using the order dydxdz. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​
D) ​ Rewrite the iterated integral using the order dydxdz. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​
E) ​ Rewrite the iterated integral using the order dydxdz. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​

F) D) and E)
G) A) and B)

Correct Answer

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The area of a region R is given by the iterated integral The area of a region R is given by the iterated integral . Switch the order of integration and show that both orders yield the same area. What is this area? A) 101 B) 20 C) 30 D) 10 E) 5 . Switch the order of integration and show that both orders yield the same area. What is this area?


A) 101
B) 20
C) 30
D) 10
E) 5

F) A) and D)
G) A) and C)

Correct Answer

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A company produces a spherical object of radius 17 centimeters. A hole of radius 4 centimeters is drilled through the center of the object. Find the outer surface area of the object.


A) A company produces a spherical object of radius 17 centimeters. A hole of radius 4 centimeters is drilled through the center of the object. Find the outer surface area of the object. A) cm<sup>3</sup><sup> </sup> B) cm<sup>3</sup><sup> </sup> C) cm<sup>3</sup><sup> </sup> D) cm<sup>3</sup><sup> </sup> E) cm<sup>3</sup><sup> </sup> cm3
B) A company produces a spherical object of radius 17 centimeters. A hole of radius 4 centimeters is drilled through the center of the object. Find the outer surface area of the object. A) cm<sup>3</sup><sup> </sup> B) cm<sup>3</sup><sup> </sup> C) cm<sup>3</sup><sup> </sup> D) cm<sup>3</sup><sup> </sup> E) cm<sup>3</sup><sup> </sup> cm3
C) A company produces a spherical object of radius 17 centimeters. A hole of radius 4 centimeters is drilled through the center of the object. Find the outer surface area of the object. A) cm<sup>3</sup><sup> </sup> B) cm<sup>3</sup><sup> </sup> C) cm<sup>3</sup><sup> </sup> D) cm<sup>3</sup><sup> </sup> E) cm<sup>3</sup><sup> </sup> cm3
D) A company produces a spherical object of radius 17 centimeters. A hole of radius 4 centimeters is drilled through the center of the object. Find the outer surface area of the object. A) cm<sup>3</sup><sup> </sup> B) cm<sup>3</sup><sup> </sup> C) cm<sup>3</sup><sup> </sup> D) cm<sup>3</sup><sup> </sup> E) cm<sup>3</sup><sup> </sup> cm3
E) A company produces a spherical object of radius 17 centimeters. A hole of radius 4 centimeters is drilled through the center of the object. Find the outer surface area of the object. A) cm<sup>3</sup><sup> </sup> B) cm<sup>3</sup><sup> </sup> C) cm<sup>3</sup><sup> </sup> D) cm<sup>3</sup><sup> </sup> E) cm<sup>3</sup><sup> </sup> cm3

F) B) and D)
G) A) and D)

Correct Answer

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Determine the diameter of a hole that is drilled vertically through the center of the solid bounded by the graphs of the equations Determine the diameter of a hole that is drilled vertically through the center of the solid bounded by the graphs of the equations if one-tenth of the volume of the solid is removed. Round your answer to four decimal places. A) 1.2983 B) 36.5966 C) 3.2983 D) 5.5966 E) 37.2983 if one-tenth of the volume of the solid is removed. Round your answer to four decimal places.


A) 1.2983
B) 36.5966
C) 3.2983
D) 5.5966
E) 37.2983

F) A) and E)
G) A) and D)

Correct Answer

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Evaluate the following improper integral. Evaluate the following improper integral. A) B) C) D) E) The integral does not converge.


A) Evaluate the following improper integral. A) B) C) D) E) The integral does not converge.
B) Evaluate the following improper integral. A) B) C) D) E) The integral does not converge.
C) Evaluate the following improper integral. A) B) C) D) E) The integral does not converge.
D) Evaluate the following improper integral. A) B) C) D) E) The integral does not converge.
E) The integral does not converge.

F) C) and D)
G) All of the above

Correct Answer

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Evaluate the iterated integral Evaluate the iterated integral by converting to polar coordinates. Round your answer to four decimal places. A) 9.2525 B) 13.2525 C) 14.2525 D) 19.2525 E) 10.2525 by converting to polar coordinates. Round your answer to four decimal places.


A) 9.2525
B) 13.2525
C) 14.2525
D) 19.2525
E) 10.2525

F) A) and E)
G) B) and D)

Correct Answer

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Find the Jacobian for the indicated change of variables. Find the Jacobian for the indicated change of variables. , A) B) C) D) E) , Find the Jacobian for the indicated change of variables. , A) B) C) D) E)


A) Find the Jacobian for the indicated change of variables. , A) B) C) D) E)
B) Find the Jacobian for the indicated change of variables. , A) B) C) D) E)
C) Find the Jacobian for the indicated change of variables. , A) B) C) D) E)
D) Find the Jacobian for the indicated change of variables. , A) B) C) D) E)
E) Find the Jacobian for the indicated change of variables. , A) B) C) D) E)

F) B) and C)
G) A) and B)

Correct Answer

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Evaluate the iterated integral Evaluate the iterated integral by converting to polar coordinates. A) B) C) D) E) by converting to polar coordinates.


A) Evaluate the iterated integral by converting to polar coordinates. A) B) C) D) E)
B) Evaluate the iterated integral by converting to polar coordinates. A) B) C) D) E)
C) Evaluate the iterated integral by converting to polar coordinates. A) B) C) D) E)
D) Evaluate the iterated integral by converting to polar coordinates. A) B) C) D) E)
E) Evaluate the iterated integral by converting to polar coordinates. A) B) C) D) E)

F) None of the above
G) A) and B)

Correct Answer

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Evaluate the following iterated integral. Evaluate the following iterated integral. A) B) C) D) E)


A) Evaluate the following iterated integral. A) B) C) D) E)
B) Evaluate the following iterated integral. A) B) C) D) E)
C) Evaluate the following iterated integral. A) B) C) D) E)
D) Evaluate the following iterated integral. A) B) C) D) E)
E) Evaluate the following iterated integral. A) B) C) D) E)

F) A) and E)
G) A) and D)

Correct Answer

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Find Find of the center of mass of the solid of given density bounded by the graphs of the equations . ​ A) B) C) D) E) of the center of mass of the solid of given density Find of the center of mass of the solid of given density bounded by the graphs of the equations . ​ A) B) C) D) E) bounded by the graphs of the equations Find of the center of mass of the solid of given density bounded by the graphs of the equations . ​ A) B) C) D) E) . ​


A) Find of the center of mass of the solid of given density bounded by the graphs of the equations . ​ A) B) C) D) E)
B) Find of the center of mass of the solid of given density bounded by the graphs of the equations . ​ A) B) C) D) E)
C) Find of the center of mass of the solid of given density bounded by the graphs of the equations . ​ A) B) C) D) E)
D) Find of the center of mass of the solid of given density bounded by the graphs of the equations . ​ A) B) C) D) E)
E) Find of the center of mass of the solid of given density bounded by the graphs of the equations . ​ A) B) C) D) E)

F) D) and E)
G) None of the above

Correct Answer

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Consider the region Consider the region in the xy-plane bounded by the ellipse and the transformation and . Find . A) B) 0 C) D) E) in the xy-plane bounded by the ellipse Consider the region in the xy-plane bounded by the ellipse and the transformation and . Find . A) B) 0 C) D) E) and the transformation Consider the region in the xy-plane bounded by the ellipse and the transformation and . Find . A) B) 0 C) D) E) and Consider the region in the xy-plane bounded by the ellipse and the transformation and . Find . A) B) 0 C) D) E) . Find Consider the region in the xy-plane bounded by the ellipse and the transformation and . Find . A) B) 0 C) D) E) .


A) Consider the region in the xy-plane bounded by the ellipse and the transformation and . Find . A) B) 0 C) D) E)
B) 0
C) Consider the region in the xy-plane bounded by the ellipse and the transformation and . Find . A) B) 0 C) D) E)
D) Consider the region in the xy-plane bounded by the ellipse and the transformation and . Find . A) B) 0 C) D) E)
E) Consider the region in the xy-plane bounded by the ellipse and the transformation and . Find . A) B) 0 C) D) E)

F) None of the above
G) A) and B)

Correct Answer

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Evaluate the improper iterated integral Evaluate the improper iterated integral . A) B) C) D) E) .


A) Evaluate the improper iterated integral . A) B) C) D) E)
B) Evaluate the improper iterated integral . A) B) C) D) E)
C) Evaluate the improper iterated integral . A) B) C) D) E)
D) Evaluate the improper iterated integral . A) B) C) D) E)
E) Evaluate the improper iterated integral . A) B) C) D) E)

F) A) and B)
G) None of the above

Correct Answer

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Evaluate the iterated integral Evaluate the iterated integral . A) B) C) D) E) .


A) Evaluate the iterated integral . A) B) C) D) E)
B) Evaluate the iterated integral . A) B) C) D) E)
C) Evaluate the iterated integral . A) B) C) D) E)
D) Evaluate the iterated integral . A) B) C) D) E)
E) Evaluate the iterated integral . A) B) C) D) E)

F) A) and B)
G) C) and E)

Correct Answer

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Identify the region of integration for the following integral. Identify the region of integration for the following integral. A) B) C) D) E)


A) Identify the region of integration for the following integral. A) B) C) D) E)
B) Identify the region of integration for the following integral. A) B) C) D) E)
C) Identify the region of integration for the following integral. A) B) C) D) E)
D) Identify the region of integration for the following integral. A) B) C) D) E)
E) Identify the region of integration for the following integral. A) B) C) D) E)

F) A) and E)
G) A) and D)

Correct Answer

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Evaluate the following iterated integral. Evaluate the following iterated integral. A) B) C) D) E)


A) Evaluate the following iterated integral. A) B) C) D) E)
B) Evaluate the following iterated integral. A) B) C) D) E)
C) Evaluate the following iterated integral. A) B) C) D) E)
D) Evaluate the following iterated integral. A) B) C) D) E)
E) Evaluate the following iterated integral. A) B) C) D) E)

F) A) and C)
G) A) and B)

Correct Answer

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Evaluate the following iterated integral. Evaluate the following iterated integral. A) 43 B) 42 C) 36 D) 33 E) 38


A) 43
B) 42
C) 36
D) 33
E) 38

F) C) and E)
G) B) and C)

Correct Answer

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Use a double integral to find the area enclosed by the graph of Use a double integral to find the area enclosed by the graph of . A) B) C) D) E) . Use a double integral to find the area enclosed by the graph of . A) B) C) D) E)


A) Use a double integral to find the area enclosed by the graph of . A) B) C) D) E)
B) Use a double integral to find the area enclosed by the graph of . A) B) C) D) E)
C) Use a double integral to find the area enclosed by the graph of . A) B) C) D) E)
D) Use a double integral to find the area enclosed by the graph of . A) B) C) D) E)
E) Use a double integral to find the area enclosed by the graph of . A) B) C) D) E)

F) C) and E)
G) B) and E)

Correct Answer

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Evaluate the integral Evaluate the integral by switching the order of integration. Round your answer to two decimal places. A) 5.16 B) 48.66 C) 15.38 D) 13.38 E) 56.14 by switching the order of integration. Round your answer to two decimal places.


A) 5.16
B) 48.66
C) 15.38
D) 13.38
E) 56.14

F) A) and B)
G) D) and E)

Correct Answer

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