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a. Let S1 be the paraboloid surface oriented in the negative x direction. Find the flux of the vector field through the surface S1.

b. Let S be the closed boundary of W. Use the Divergence Theorem to find the total flux out of S.

divF = dF1/dx + dF2/dy + dF3/dz

fluxF = Int(FdA) = Int(divFdV) (Sorry, the integral tags aren't working for me.)

I found the divF easily enough to be 5, but when I try to use that to calculate the flux, the online homework says that I'm wrong.

Int(divFdV) should be the integral of 5 over the volume of the paraboloid, which is x from 0 to 16, y from -4 to 4, and z from -4 to 4. Integrating over x gives 80, then over y gives 640, then over z gives 5120, which should be the answer. I tried -5120 as well, since it says the surface is oriented in the negative x direction, but that is also wrong. Can anybody tell me what I'm messing up? Also, once I find the flux, that should be the answer for both questions, right?

Sorry for the somewhat messy explanation of my work, I'm not used to explaining my process without being able to draw things out.