(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Verify Stokes Theorem ∬(∇xF).NdA where surface S is the paraboloid z = 0.5(x^2 + y^2) bound by the plane z=2, Cis its boundary, and the vector field F = 3yi- xzj+ yzk.

3. The attempt at a solution

I had found (∇xF) = (z+x)i+ (-z-3)k

r = [u, v, 0.5(u^2 + v^2)]

ThereforeN= ru X rv = -ui-uj+k

Therefore (∇xF).N= [(z+x), 0, (-z-3)].[-x, -y, 1]

After that I substitute x = rcos(θ), y = rsin(θ), z = 0.5r^2

Thus ∫(0-2)∫(0-2pi) (∇xF).Nr dθdr

But I cant seems to get the answer. Can anyone help? Help would greatly appreciated :)

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# Homework Help: Stokes Theorem

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