Question: Compute (iint_{mathcal{S}} mathbf{F} cdot d mathbf{S}) for the given oriented surface. (mathbf{F}=y^{2} mathbf{i}+2 mathbf{j}-x mathbf{k}), portion of the plane (x+y+z=1) in the octant (x, y,

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

\(\mathbf{F}=y^{2} \mathbf{i}+2 \mathbf{j}-x \mathbf{k}\), portion of the plane \(x+y+z=1\) in the octant \(x, y, z \geq 0\), upward-pointing normal

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