Question: Compute (iint_{mathcal{S}} mathbf{F} cdot d mathbf{S}) for the given oriented surface or parametrized surface. (mathbf{F}(x, y, z)=leftlangle y, x, e^{x z}ightangle, quad x^{2}+y^{2}=9, x geq

Compute \(\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}\) for the given oriented surface or parametrized surface.

\(\mathbf{F}(x, y, z)=\left\langle y, x, e^{x z}ightangle, \quad x^{2}+y^{2}=9, x \geq 0, y \geq 0\), \(-3 \leq z \leq 3\), outward-pointing normal

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