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Math Help - Peicewise Smooth curve

  1. #1
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    Peicewise Smooth curve

    Let f = u + iv be a contiunous function and o(t) = x(t) + iy(t) be a piecewise smooth curve...

    Show that Re{ integral (f(z) dz } = integral (udx - vdy)

    How do I show this?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by jzellt View Post
    Let f = u + iv be a contiunous function and o(t) = x(t) + iy(t) be a piecewise smooth curve...

    Show that Re{ integral (f(z) dz } = integral (udx - vdy)

    How do I show this?
    What have you tried? Also, you need to be more describitive. Are we trying to prove that \text{Re}\int_\Gamma f(z) dz=\int_{\Gamma}\left(u\text{ }dx-v\text{ }dy\right)?
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  3. #3
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    Yes, that I want Im trying to show.

    I really don't know how to approach this problem, so I havn't done anything.

    I was hoping to see how this one is done so I can do a similiar proof (the imaginary part) by myself...

    Please help
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