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We are nearing the end of our course --- culminating in Stokes and Divergence Theorems for surface integrals, and I am having some difficulty with the following

1. F(x,y,z) = [tex]<x^3y, -x^2y^2, -x^2yz>[/tex]

where S is the solid bounded by the hyperboloid x^2 + y^2 - z^2 =1 and the planes z = -2 and z=2.

I computed div F properly...

Well I know what the z limits are in my Triple Integral, however what must I use as my radius? Theta should go from 0 to 2pi correct?

2. F(x,y,z) = [tex]<x^2y, xy^2, 2xyz>[/tex]

where S is the surface of the tetrahedron bounded by the planes x=0, y=0, z=0, and x+2y+z = 2

Here must my triple integral be from 0 to 2 for the x limit, then 0 to (2-x)/2 for my y limits, and for z just 0 to 2-x-2y.

Those seem correct, but a confirmation would be nice! Thanks a lot!

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# Help with using the Divergence Theorem!

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