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.

\(\mathbf{F}=\left\langle e^{z^{2}}-y, e^{z^{3}}+x, \cos (x z)ightangle\), the upper half of the unit sphere \(x^{2}+y^{2}+z^{2}=1, z \geq 0\) with outwardpointing normal

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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 S. If S is a closed surface, then Ils curl(F). ds = 0 1