# Simple Surface Integral

1. Apr 13, 2008

### cpfoxhunt

1. The problem statement, all variables and given/known data

This is annoying me because I am so clearly being a muppet somewhere. I need to integrate the vector field (x,-y,z).(vector)ds over the surface of a cyliner x^2 + y^2 < 4 (or equal to) and z is between 0 and 1.

3. The attempt at a solution

I have to do it both with and without divergence. With divergence, div(a) = 1, integral over a nice volume, gives me 4Pi, as O a, (integrating 2*r drd(theta)dz, with the specified limits.)

Trying to do it as a surface integral is driving me nuts. I end up integrating r^2(sin^2(x) - cos^(x) between the limits x = 0 and x = pi. as this integrates to sin(x)cos(x), this makes the entire integral zero.

So where am I going wrong?

2. Apr 13, 2008

### Dick

I don't think you included the contributions from the flat ends of the cylinder, did you?