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 z, 0, z^{2}ightangle, quad Phi(u, v)=(v cosh u,

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

$\mathbf{F}(x, y, z)=\left\langle z, 0, z^{2}ightangle, \quad \Phi(u, v)=(v \cosh u, v \sinh u, v), 0 \leq u \leq 1,0 \leq v \leq 1, \quad$ upward-pointing normal

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