Use the Divergence Theorem to calculate (iint_{mathcal{S}} mathbf{F} cdot d mathbf{S}) for the given vector field and

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Use the Divergence Theorem to calculate \(\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}\) for the given vector field and surface.

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\(\mathbf{F}(x, y, z)=\left\langle x y z+x y, \frac{1}{2} y^{2}(1-z)+e^{x}, e^{x^{2}+y^{2}}ightangle, \mathcal{S}\) is the boundary of the solid bounded by the cylinder \(x^{2}+y^{2}=16\) and the planes \(z=0\) and \(z=y-4\).

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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