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August 9th, 2017, 12:29 AM   #1
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Flux of vector field

I have F(x,y,z)=(z,0,2) and i need to find the flux through the upper side of the paraboloid z=2-x^2-y^2 1<z<2.
When solving this with Gaussian theorem (divergence theorem) I'm not sure whether z will be = to 1 or 2?
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August 9th, 2017, 03:29 AM   #2
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The 'upper side' of the paraboloid is neither z= 1 nor z= 2, it is the paraboloid! The paraboloid has vertex at (0, 0, 2) and opens downward. In order to make it a closed surface, so that you can use the divergence theorem, you would add the plane z= 1.
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