Calculate (iint_{mathcal{S}} f(x, y, z) d S) for the given surface and function. (Phi(u, v)=(u cos v,
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Calculate \(\iint_{\mathcal{S}} f(x, y, z) d S\) for the given surface and function.
\(\Phi(u, v)=(u \cos v, u \sin v, u), \quad 0 \leq u \leq 1, \quad 0 \leq v \leq 1 ; f(x, y, z)=z\left(x^{2}+y^{2}ight)\)
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