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## Homework Statement

Verify Stokes Theorem ∬(∇xF).

**N**dA 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 = 3y

**i**- xz

**j**+ yz

**k**.

## The Attempt at a Solution

I had found (∇xF) = (z+x)

**i**+ (-z-3)

**k**

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

Therefore

**N**= ru X rv = -u

**i**-u

**j**+

**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).

**N**r dθdr

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