# 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:

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