Question: Compute (iint_{mathcal{S}} mathbf{F} cdot d mathbf{S}) for the given oriented surface or parametrized surface. (mathbf{F}(x, y, z)=langle 0,0, zangle, quad 3 x^{2}+2 y^{2}+z^{2}=1, quad z

Compute $\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}$ for the given oriented surface or parametrized surface.
$\mathbf{F}(x, y, z)=\langle 0,0, zangle, \quad 3 x^{2}+2 y^{2}+z^{2}=1, \quad z \geq 0$, upward-pointing normal

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solution We use modified spherical coordinates to parametrize the ellipsoid Phitheta phileftfrac1sqrt3 cos theta sin phi frac1sqrt2 sin theta sin phi ... View full answer

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