Question: Compute (iint_{mathcal{S}} mathbf{F} cdot d mathbf{S}) for the given oriented surface. (mathbf{F}=langle x, y, zangle, quad) part of sphere (x^{2}+y^{2}+z^{2}=1), where (frac{1}{2} leq z leq

Compute $\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}$ for the given oriented surface.

$\mathbf{F}=\langle x, y, zangle, \quad$ part of sphere $x^{2}+y^{2}+z^{2}=1$, where $\frac{1}{2} \leq z \leq \frac{\sqrt{3}}{2}, \quad$ inward-pointing normal

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