Deck 14: Section 6: Multiple Integration

Question 1

Find the center of mass of the solid bounded by and with density function .

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B)
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D)
E)

Answer 1

Question 2

Evaluate the iterated integral .

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B)
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D)
E)

Answer 2

Question 3

Find of the center of mass of the solid of given density bounded by the graphs of the equations .

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D)
E)

Answer 3

Question 4

Find the average value of over the region Q, where Q is a cube in the first octant bounded by the coordinate planes, and the planes and . The average value of a continuous function over a solid region Q is , where V is the volume of the solid region Q.

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D)
E)

Question 5

Find the centroid of the solid region bounded by the graphs of the equations. Use a computer algebra system to evaluate the triple integral. (Assume uniform density and find the center of mass.)

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E)

Question 6

Find the average value of over the region Q, where Q is a tetrahedron in the first octant with vertices and . The average value of a continuous function over a solid region Q is , where V is the volume of the solid region Q.

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B)
C)
D)
E)

Question 7

Use a triple integral to find the volume of the solid bounded by the graphs of the equations .

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B)
C)
D)
E)

Question 8

Evaluate the following iterated integral.

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D)
E)

Question 9

Find for the indicated solid with density function .

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D)
E)

Question 10

Evaluate the following iterated integral.

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E)

Question 11

Set up a triple integral for the volume of the solid bounded above by the cylinder and below by the paraboloid .

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D)
E)

Question 12

Determine the value of b so that the volume of the ellipsoid is .

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E)

Question 13

Set up a triple integral that gives the moment of inertia about the -axis of the solid region Q of density given below.

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E)

Question 14

Use a triple integral to find the volume of the solid shown below.

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D)
E)

Question 15

Use a triple integral to find the volume of the solid shown below.

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D)
E)

Question 16

Rewrite the iterated integral using the order .

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E)

Question 17

Set up a triple integral for the volume of the solid bounded by and .

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B)
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D)
E)

Question 18

Sketch the solid whose volume is given by the iterated integral given below and use the sketch to rewrite the integral using the indicated order of integration. Rewrite the integral using the order .

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D)
E)

Question 19

Set up a triple integral for the volume of the solid bounded by the coordinate planes and the plane given below.

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B)
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D)
E)