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.

\(\mathbf{F}=\langle y z, x z, x yangle\), that part of the cylinder \(x^{2}+y^{2}=1\) that lies between the two planes \(z=1\) and \(z=4\) with outward-pointing 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. fos F.dr - curl(F). dS The integral on the left is defined relative to the boundary orientation of 85. If S is a closed surface, then Js curl(F). dS=0 1