Suppose that surface $\sigma$ is parameterized by

$r(u,v) = \left$, $0\leq u\leq 6$ and $0 \leq v\leq \frac {1\pi}{3}$
and $f(x,y,z) = x^{2}+y^{2}+z^{2}$. Set up the surface integral (you don't need to evaluate it).

 $\displaystyle\int\limits_\sigma\!\!\int f(x,y,z)\,dS = \int\limits_R\!\!\int f\left(x(u,v),y(u,v),z(u,v)\right)\left\Vert\frac{\partial r}{\partial u}\times\frac{\partial r}{\partial v}\right\Vert dA$
 = $\displaystyle\int$ $\displaystyle\int$ $\Bigg\Vert$ $\Bigg\Vert\hskip 3pt du\,dv$

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