# Surface Integral of Two Surfaces

1. Dec 12, 2004

### Lomion

Hello!

This is a question from one of our past exams, and it's had me stumped for the past hour. The question states:

The cylinder $$x^2+y^2=2x$$ cuts out a portion of a surface S from the upper nappe of the cone $$x^2+y^2=z^2$$.

Compute the surface integral: $$\int\int (x^4-y^4+y^2z^2-z^2x^2+1) dS$$

I'm mainly having trouble getting started. What exactly is the surface that we're supposed to evaluate the integral over?

My guess on this question is that I should parametrize the cone:
$$T(u,v) = (vcosu, vsinu, v)$$

And use that to find $$T_u X T_v$$.

But what do I do after this? In order to find the limits of integration for u and v, do I use the conditions given by the cylinder? $$v = 2cosu$$?

Using that still doesn't give me the numerica limits for v, though.

Help, anyone?

Last edited: Dec 12, 2004