Deck 14: Section 8: Multiple Integration

Question 1

Sketch the image S in the uv-plane of the region R in the xy-plane using the given transformation.

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B)
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D)
E)

Answer 1

Question 2

If and then the Jacobian of x, y, and z with respect to u, v, and w is .
Find the Jacobian for the following change of variables:

A)
B)
C)
D)
E)

Answer 2

Question 3

Find the Jacobian for the change of variables given below.

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D)
E)

Answer 3

Question 4

Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R: region bounded by the square with vertices .

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D)
E)

Question 5

Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R: region bounded by the parallelogram with vertices . Round your answer to two decimal places.

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D)
E)

Question 6

Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R: region bounded by the graphs of (Hint: Let .) Round your answer to two decimal places.

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B)
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D)
E)

Question 7

Find the Jacobian for the indicated change of variables.

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B)
C)
D)
E)

Question 8

Consider the region in the xy-plane bounded by the ellipse and the transformation and . Find .

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B)
C)
D)
E)

Question 9

Find the Jacobian for the following change of variables:

A)
B)
C)
D)
E)

Question 10

Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R: region bounded by the parallelogram with vertices . Round your answer to two decimal places.

A)
B)
C)
D)
E)

Question 11

If and then the Jacobian of x, y, and z with respect to u, v, and w is . Find the Jacobian for the following change of variables:

A)
B)
C)
D)
E)

Question 12

Use the indicated change of variables to evaluate the following double integral.

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B)
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D)
E)

Question 13

Find the Jacobian for the following change of variables:

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B)
C)
D)
E)

Question 14

Use the indicated change of variables to evaluate the following double integral.

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B)
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D)
E)

Question 15

Use the following change of variables to evaluate the double integral . Round your answer to four decimal places.

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D)
E)

Question 16

Find a transformation that when applied to region , its image will be .

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D)
E)

Question 17

Consider the region R in the xy-plane bounded by the ellipse and the transformation and . Find the area of the ellipse. Round your answer to two decimal places.

A)
B)
C)
D)
E)

Question 18

Find the Jacobian for the following change of variables:

A)
B)
C)
D)
E)

Question 19

Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R. R: region bounded by the triangle with vertices

A)
B)
C)
D)
E)