Sun K.

asked • 03/24/13

Use the Divergence Theorem to compute the surface integral?

Use the Divergence Theorem to compute the surface integral where Q is bounded by z=x^2+y^2 and z=4, F=<x^3, y^3-z, xy^2>. (Answer: 32pi)

The divergence of the vector field is 3x^2+3y^2, which I've found.

How should I set up the triple integral and find the points of the integral and solve for it?

And where did you get 2*pi*r from?

Sun K.

How did you get from 0 to sqrt(z)?

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03/24/13

Robert J.

z = x^2+y^2 = r^2

r = sqrt(z)

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03/24/13

Sun K.

But where did you get the 2*pi*r from?

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03/24/13

Robert J.

dxdy = rd?dr

Integrating d? from 0 to 2pi gives dxdy = 2pi*r dr

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03/24/13

Robert J.

? = theta. I don't know why it was changed to "?"

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03/24/13

Sun K.

Okay. Thanks.

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03/24/13

1 Expert Answer

By:

Robert J. answered • 03/24/13

Certified High School AP Calculus and Physics Teacher

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