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Math Help - Stoke's Theorem

  1. #1
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    Stoke's Theorem

    Evaluate the line integral
    I = (x2z + yzexy) dx + xzexy dy + exy dz

    where C is the arc of the ellipse r(t) = (cost,sint,2−sint) for 0 <= t <= PI.
    [Hint: Do not compute this integral directly. Find a suitable surface S such that C is a part of the boundary ∂S and use Stokesí theorem.]



    Because this is from 0 to Pi, this is an open curve? Can you compute the integral using stokes theorem over the surface from 0 to 2Pi, so you have a closed curve and then divide that answer by two to get the open curve 0 to Pi?
    I'm confused on what techniques to use when the curve is open.

    any help would be wonderful. Thanks in advance!
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  2. #2
    MHF Contributor
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    Check the 6 partial derivatives first to see if it is conservative. If so, the integral will be zero.

    If not,

    \iint\mathbf{curl}\cdot\mathbf{k}
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