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Applying Stoke's Theorem to a parabaloid

  1. Oct 3, 2012 #1
    1. The problem statement, all variables and given/known data
    Let S be the surface defined by y=10−x^2−z^2 with y≥1, oriented with rightward-pointing normal. Let F=(2xyz+5z)i+e^(x)cosyzj+(x^2)yk. Determine ∫∫∇×F·dS.

    2. Relevant equations

    ∫∫∇×F·dS = ∫F·dS

    3. The attempt at a solution
    I think the boundary of the surface is the circle of radius √5 in the xz plane. The parameterization of this should be equal to <√5cost,0,√5sint>. After plugging this parameterization into F and taking the dot product with dS I got ∫-25sin2tdt from 0 to 2 pi, which equals -25∏, however this is not the correct answer. I am not sure about what I am doing wrong. I would appreciate any assistance.
  2. jcsd
  3. Oct 3, 2012 #2


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    hi mlb2358! :smile:

    (try using the X2 button just above the Reply box :wink:)
    nooo … :wink:
  4. Oct 3, 2012 #3


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    Reread your problem. What is the restriction on y?
  5. Oct 3, 2012 #4


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    And think about the orientation.
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