\begin{equation} \iint_S z+x^2y \,\, dS \end{equation} Where S is the part of the cylinder $y^2+z^2=1$ that lies between the planes $x=0$ and $x=3$ in the first octant.
I tried to convert to Polar coordinates $S=\{ (r,\theta) | 0\leq r\leq1, \,\,0\leq\theta\leq\pi/2\}$. This gives me: \begin{equation} \iint_S (\sqrt{1-\sin(\theta)^2}+\cos(\theta)^2\sin(\theta))r \,\, d\theta dr \end{equation}
Which I have no idea how to integrate. Any hints for setting this up?