• Support PF! Buy your school textbooks, materials and every day products Here!

Stokes Theorem problem

  • #1

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!!:confused:
 
Last edited:

Answers and Replies

  • #2
392
0
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
Dick
Science Advisor
Homework Helper
26,258
618
What function do you get that you can't integrate? It looks like it's just a trig substitution to me.
 
  • #4
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
Dick
Science Advisor
Homework Helper
26,258
618
Yes, it's pi. Both ways.
 

Related Threads for: Stokes Theorem problem

  • Last Post
Replies
3
Views
5K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
3
Views
464
  • Last Post
Replies
7
Views
896
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
1
Views
706
  • Last Post
2
Replies
27
Views
3K
Top