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Suppose F⃗ (x,y,z)=⟨x,y,5z⟩. Let W be the solid bounded by the paraboloid z=x2+y2 and the plane z=4. Let S be the closed boundary of W oriented outward.

(a) Use the divergence theorem to find the flux of F⃗ through S.

∬

_{s}F⃗ ⋅dA⃗ =

**56pi**

**(b) Find the flux of F⃗ out the bottom of S (the truncated paraboloid) and the top of S (the disk).**

Flux out the bottom =

Flux out the top =

Flux out the bottom =

Flux out the top =

Thanks for your help.

BTW, side question. What exactly is the difference in the Surface and Flux integral.