# Homework Help: Surface Integral over a Cone - Stokes?

1. Nov 11, 2012

### YayMathYay

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

2. Relevant equations

I'm guessing Stoke's Theorem? However, I'm not sure how to apply it exactly..

3. The attempt at a solution

Looking at Stoke's Theorem, I'm still not sure how to apply it. I'm really just lost as to where to begin; is there even a $\grad F$ to take? I know this is related to Stoke's (I hope), but not sure how to begin.

Last edited: Nov 11, 2012
2. Nov 11, 2012

### Dick

It doesn't look like Stoke's to me. I don't see any vectors anywhere. Your first job is to figure out what dA is in terms of dx*dy. Then a change to polar coordinates might make it easier to do the dx*dy integral. It's actually pretty straight forward.

Last edited: Nov 11, 2012
3. Nov 11, 2012

### YayMathYay

I also am trying this formula:

But I'm not getting to 9pi.. I'm not sure what the difference between f(x, y, z) and f(x, y, g(x, y)) is.

4. Nov 11, 2012

### Dick

That's the right direction. Your g(x,y) is just z. Solve your equation for z^2 for z to get g(x,y). It's sqrt(3)*sqrt(x^2+y^2), right?

5. Nov 11, 2012

### YayMathYay

I did, that and my integrand on the right side came out to be 2(x^2 + y^2).

But I don't see how to get to the correct answer from that.

6. Nov 11, 2012

### Dick

Ok. That's good. The easiest way to do it from here is to change to polar coordinates. Did you try that?

7. Nov 11, 2012

### YayMathYay

Yes. But if I change to polar, I get 18pi, because of the 2 there.

8. Nov 11, 2012

### Dick

Which 2? Show your work, ok?

9. Nov 11, 2012

### YayMathYay

Urgh, I just didn't want to type it out because I don't know how to use LaTeX and it looks messy.

Integrand: 2(x^2 + y^2) dx dy

Changed to polar w/:
x = sqrt(3) * cos t
y = sqrt(3) * sin t

New Integrand: 6r dr dt [r from 0 to sqrt(3), t from 0 to 2pi]

10. Nov 12, 2012

### Dick

And there's your problem. The integrand is supposed to be integrated over r. You don't put a specific value of r in. x^2+y^2 is just r^2.