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 0,0, x^{2}+y^{2}ightangle, quad x^{2}+y^{2}+z^{2}=4, quad z geq 0),

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

\(\mathbf{F}(x, y, z)=\left\langle 0,0, x^{2}+y^{2}ightangle, \quad x^{2}+y^{2}+z^{2}=4, \quad z \geq 0\), outward-pointing normal

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