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Verification Of Stoke's Theorem

  1. May 5, 2013 #1
    1. The problem statement, all variables and given/known data
    Verify Stoke's Theorem by computing both integrals: (stoke's theorem, and the original work integral).
    σ is the portion of z = sqrt(4-x2-y2) above the xy-plane and the vector field is F = <2x-y, y*z2, y2z>

    2. Relevant equations
    stoke's theorem, and work integral


    3. The attempt at a solution
    When I do stoke's theorem I get <0,0,1> for my curl F. My normal vector is <2x, 2y, 2z>. After I do the two, and do the integral I get 33.51 for my answer.

    My work integral I have <2cos(t), 2sin(t)> for my parametrization path. However, when I do the integral I get 12.5. I am not sure which one is right since I have tried the problem three times, but I always get the same answer, so I do not know what to do.
     
  2. jcsd
  3. May 5, 2013 #2

    LCKurtz

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    Do you expect us to work both sides out to see what we get? Show us what you did and we can likely quickly find your mistake.
     
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