Calculate curl(F) and then apply Stokes' Theorem to compute the flux of \(\operatorname{curl}(\mathbf{F})\) through the given surface using a line integral.

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(\mathbf{F}=\langle 3 z, 5 x,-2 yangle\), that part of the paraboloid \(z=x^{2}+y^{2}\) that lies below the plane \(z=4\) with upwardpointing unit normal vector

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THEOREM 1 Stokes' Theorem Let S be a surface as described earlier, and let F be a vector field whose components have continuous partial derivatives on an open region containing S. kos = = ]] F.dr= curl(F). dS The integral on the left is defined relative to the boundary orientation of aS. If S is a closed surface, then Ja curl(F)-dS=0 1