# Stokes Theorem problem

## Homework Statement

F = xi + x3y2j + zk; C the boundary of the semi-ellispoid z = (4 - 4x2 - y2)1/2 in the plane z = 0

## Homework Equations

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

double integral (curl F) . n ds

## 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:

## Answers and Replies

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

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

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

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?

Dick
Science Advisor
Homework Helper
Yes, it's pi. Both ways.