How to use Gauss Divergence theorem to evaluate the surface integral over the portion of z=9-x^2-y^2 with z>=0?

Question : Use Gauss Divergence theorem to evaluate the surface integral over the portion of z=9-x^2-y^2 with z>=0 \[\iint_{\gamma}{\left(\nabla\ \times\ \vec{F}\right).\hat{n}\ dS\ }\]where\[ \vec{F}\ =\ (y-z)\ \hat{i}-(x+z)\hat{j}\ +\ (x+y)\ \hat{k} \]γ is the portion of \[z =\ 9-x^2\ \ -y^2\]…

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