Calculate (iint_{mathcal{S}}left(x^{2}+y^{2}ight) e^{-z} d S), where (mathcal{S}) is the cylinder with equation (x^{2}+y^{2}=9) for (0 leq z
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Calculate \(\iint_{\mathcal{S}}\left(x^{2}+y^{2}ight) e^{-z} d S\), where \(\mathcal{S}\) is the cylinder with equation \(x^{2}+y^{2}=9\) for \(0 \leq z \leq 10\).
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