Let (mathcal{S}) be the portion of the sphere (x^{2}+y^{2}+z^{2}=9), where (1 leq x^{2}+y^{2} leq 4) and (z

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Let \(\mathcal{S}\) be the portion of the sphere \(x^{2}+y^{2}+z^{2}=9\), where \(1 \leq x^{2}+y^{2} \leq 4\) and \(z \geq 0\) (Figure 20). Find a parametrization of \(S\) in polar coordinates and use it to compute:
(a) The area of \(\mathcal{S}\)
(b) \(\iint_{\mathcal{S}} z^{-1} d S\)

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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