Verify Stokes' Theorem for the given vector field and surface, oriented with an upwardpointing normal.

\(\mathbf{F}=\langle 2 x y, x, y+zangle\), the surface \(z=1-x^{2}-y^{2}\) for \(x^{2}+y^{2} \leq 1\)

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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. s r = SS curl(F). ds F.dr= The integral on the left is defined relative to the boundary orientation of S. If S is a closed surface, then Is curl(F) - ds = 0 1