Question
In Exercises $5-17,$ compute $\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}$ for the given oriented surface.$\mathbf{F}=\langle z, z, x\rangle, \quad z=9-x^{2}-y^{2}, x \geq 0, y \geq 0, z \geq 0, \quad$ upward-pointing normal
Step 1
We can do this by taking the cross product of the partial derivatives of the surface with respect to x and y. The surface is given by $z = 9 - x^2 - y^2$, so we have: \[ \frac{\partial z}{\partial x} = -2x, \quad \frac{\partial z}{\partial y} = -2y \] The normal Show more…
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