I want to solve the following problem, I want to find
$ \iint_S x \, \mathrm{d}S $ where S is the part of the parabolic cylinder that lies inside of the cylinder $z = x^2/2$, and in the first octant of the cylinder $x^2 + y^2 = 1$
I was obviously thinking about switching to cylindrical coordinates, but I have problems setting up the problem and finding the limits.
Could I get some tips / help ? =)