# Stokes Theorem problem

1. Apr 19, 2009

### astonmartin

1. The problem statement, all variables and given/known data
F = xi + x3y2j + zk; C the boundary of the semi-ellispoid z = (4 - 4x2 - y2)1/2 in the plane z = 0

2. Relevant equations

(don't know how to write integrals on here, sorry)

double integral (curl F) . n ds

3. The attempt at a solution

curl F = 3y2x2k
n = k

curl F . n = 3y2x2

So I have a surface integral, which I think I can change to dA since the differential of the surface area is just 1dA...

Now this is where I'm stuck. How do i do the double integral with an ellipse? I tried it in rectangular coordinates but got some function I don't know how to integrate. Help!!

Last edited: Apr 19, 2009
2. Apr 20, 2009

### Billy Bob

Can you do this by integrating F dot dr over the boundary curve instead?

r(theta)=cos(theta) I+2sin(theta) J+0 K

3. Apr 20, 2009

### Dick

What function do you get that you can't integrate? It looks like it's just a trig substitution to me.

4. Apr 20, 2009

### cartonn30gel

what you can do is use Stoke's theorem to convert to the line integral of the vector filed and then if you use Green's theorem to convert that to a double integral, use a trig sub and then integrate. (integration takes a little bit of work) I think the answer is pi. Anybody agree?

5. Apr 20, 2009

### Dick

Yes, it's pi. Both ways.