surface integral question

[Matt R.]

I have a mathematical physics final tomorrow, and I'm having trouble with surface integrals. I can't reach my prof through email, so I was hoping someone here could help me. Here is an example question:

If F = 2y i - z j + x^2 k and S is the surface of the parabolic cylinder y^2 = 8x in the first octant bounded by the planes y = 4 and z = 6, evaluate:

|| F.n dS

The || is just a double integral over the surface S, and F.n is the force vector dotted with the normal.

Essentially what I am stuck on is expressing the given surface as a vector function so I can dot it with the force. Or alternatively, finding the normal to such a surface to get F.n and finding dS. I don't have any trouble if I am given the surface expressed as a vector function, but I don't know how to convert.

Thanks for any help in advance.