Deck 15: Section 7: Vector Analysis

Question 1

Evaluate , where and S is the closed surface of the solid bounded by the graphs , , and the coordinate planes.

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D)
E)

Answer 1

Question 2

Let and let S be the surface bounded by and . Verify the Divergence Theorem by evaluating as a surface integral and as a triple integral. Round your answer to two decimal places.

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B)
C)
D)
E)

Answer 2

Question 3

Evaluate where S is the closed surface of the solid bounded by the graphs of

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B)
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D)
E)

Answer 3

Question 4

Use Divergence Theorem to evaluate and find the outward flux of through the surface S of the solid bounded by the planes

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B)
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D)
E)

Question 5

Use Divergence Theorem to evaluate and find the outward flux of through the surface S of the solid bounded by the planes .

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B)
C)
D)
E)

Question 6

Let and let S be the cylinder Verify the Divergence Theorem by evaluating as a surface integral and as a triple integral.

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D)
E)

Question 7

Use the Divergence Theorem to evaluate Verify your answer by evaluating the integral as a triple integral. S: cube bounded by the planes

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E)

Question 8

Use Divergence Theorem to evaluate and find the outward flux of through the surface S of the solid bounded by the sphere .

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E)

Question 9

Use the Divergence Theorem to evaluate and find the outward flux of through the surface of the solid bounded by the graphs of the equations. Use a computer algebra system to verify your results.

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B)
C)
D)
E)

Question 10

Let and let S be the surface bounded by the plane and the coordinates planes. Verify the Divergence Theorem by evaluating as a surface integral and as a triple integral.

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B)
C)
D)
E)

Question 11

Use Divergence Theorem to evaluate and find the outward flux of through the surface S of the solid bounded by and .

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B)
C)
D)
E)

Question 12

Use the Divergence Theorem to evaluate and find the outward flux of through the surface of the solid bounded by the graphs of the equations. Use a computer algebra system to verify your results.

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B)
C)
D)
E)

Question 13

Use Divergence Theorem to evaluate and find the outward flux of through the surface S of the solid bounded by

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B)
C)
D)
E) 0

Question 14

Let and let S be the surface bounded by and . Verify the Divergence Theorem by evaluating as a surface integral and as a triple integral. Round your answer to two decimal places.

A)
B)
C)
D)
E)

Question 15

Let and let S be the cube bounded by the planes . Verify the Divergence Theorem by evaluating as a surface integral and as a triple integral.

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B)
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D)
E)

Question 16

Let and let S be the surface bounded by the planes and the coordinate planes. Verify the Divergence Theorem by evaluating as a surface integral and as a triple integral. Round your answer to two decimal places wherever applicable.

A)
B)
C)
D)
E)

Question 17

Use Divergence Theorem to evaluate and find the outward flux of through the surface S of the solid bounded by the planes .

A)
B)
C)
D)
E)

Question 18

Use the Divergence Theorem to evaluate and find the outward flux of through the surface of the solid bounded by the graphs of the equations. Use a computer algebra system to verify your results.

A)
B)
C)
D)
E)