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Let S be the cone z = 4 − ( x^2 + y^2)^(1/2) where z ≥...

Let S be the cone z = 4 − ( x^2 + y^2)^(1/2) where z ≥ 0, oriented with downward pointing unit normal vectors. The image below contains S. The grey plane is the xy-plane. Let F~ (x, y, z) = <− z , x − y , x + y >. Use Stokes’ Theorem to evaluate Z Z S ∇ × F~ · dS~.

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