Calculate curl(F) and then apply Stokes' Theorem to compute the flux of curl ( F ) curl

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

\(\left.\mathbf{F}=\left\langle x+y, z^{2}-4, x \sqrt{y^{2}+1}ight)ightangle\), surface of the wedge-shaped box in Figure 15 (bottom included, top excluded) with outward-pointing 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. Jas = = ]] 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