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Stokes Theorem problem

  1. Apr 19, 2009 #1
    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!!:confused:
    Last edited: Apr 19, 2009
  2. jcsd
  3. Apr 20, 2009 #2
    Can you do this by integrating F dot dr over the boundary curve instead?

    r(theta)=cos(theta) I+2sin(theta) J+0 K
  4. Apr 20, 2009 #3


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    What function do you get that you can't integrate? It looks like it's just a trig substitution to me.
  5. Apr 20, 2009 #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?
  6. Apr 20, 2009 #5


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    Yes, it's pi. Both ways.
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