Compute (iint_{mathcal{S}} mathbf{F} cdot d mathbf{S}) for the given oriented surface. (mathbf{F}=leftlangle e^{z}, z, xightangle, quad Phi(r,
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Compute \(\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}\) for the given oriented surface.
\(\mathbf{F}=\left\langle e^{z}, z, xightangle, \quad \Phi(r, s)=(r s, r+s, r)\), \(0 \leq r \leq 1,0 \leq s \leq 1, \quad\) oriented by \(\mathbf{T}_{r} \times \mathbf{T}_{s}\)
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