# Surface Integral

1. May 5, 2013

### Baumer8993

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

Evaluate ∫∫σ3x2 + 3y2 + 3z2 dS
where σ is the part of the cylinder x2 + y2 = 4 between the planes z = 0
, and z = 1, together with the top, and bottom disks.

2. Relevant equations
Surface integrals, maybe divergence theorem?

3. The attempt at a solution
I am having trouble knowing where to start with this one. I think I need to do a surface integral, but maybe with more than one surface? If that is right then what would I do for the cylinder side? How would I handle the z in the integral?

2. May 5, 2013

### SteamKing

Staff Emeritus
What is the value of z at the top and bottom of the cylinder?

What is the equation of the surface in between the top and bottom disks? Hint: it's a constant

3. May 5, 2013

### haruspex

I would start the integration over the curved surface by converting to cylindrical coordinates.

4. May 6, 2013

### Baumer8993

Ok so I see that z = 0, and z = 1. What about the sides? Do I have to do them in three separate integrals?

5. May 6, 2013

Yes.