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Math Help - Stokes Theorem :( help me

  1. #1
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    Stokes Theorem :( help me

    Stokes Theorem :( help me-132.png
    Stokes Theorem :( help me-2013-09-21-16.33.37.jpg
    First is the problem and next one is my sols.

    but it doesn't satisfy Stokes' Theorem S curl(F)*dA= Sc F*dl

    surface integral = 0, Line integral (with x^2+y^2=1) = 2pi

    what's wrong with me
    Last edited by Yoon; September 20th 2013 at 11:52 PM.
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  2. #2
    MHF Contributor

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    Re: Stokes Theorem :( help me

    Well, I can't speak to what's wrong with you! But here, you have a sign error.
    \nabla\times F= \left|\begin{array}{ccc}\vec{ix} & \vec{j} & \vec{k} \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\ \frac{-y}{x^2+y^2} & \frac{x}{x^2+y^2} & 0 \end{array}\right|
    = \left(\frac{\partial}{\partial x} \left(\frac{x}{x^2+ y^2}\right)- \frac{\partial}{\partial y}\frac{-y}{x^2+y^2}\right)\vec{k}
    With those two "-" signs, the partial derivatives add:
    \left(\frac{y^2- x^2}{(x^2+ y^2)}+ \frac{y^2- x^2}{(x^2+ y^2)}\right)\vec{k}= 2\frac{y^2- x^2}{(x^2+ y^2)}\vec{k}
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