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Math Help - Convert line integral to surface integral

  1. #1
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    Convert line integral to surface integral

    Hello!

    I have problem with converting line integral to surface integral of functions in polar coordinates.

    Here are two examples

    Convert line integral to surface integral-codecogseqn-1-.gif

    and
    Convert line integral to surface integral-codecogseqn-2-.gif

    How can I convert this two line integrals to surface integrals.

    w and v are functions w = w(r, phi) and v = v(r, phi)

    Thanks for help!
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  2. #2
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    Re: Convert line integral to surface integral

    IF these are closed paths then you can convert to a surface integral over the region they bound, using Stoke's theorem. If they do not, you could "close" the paths in an infinite number of ways give different representations.
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  3. #3
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    Re: Convert line integral to surface integral

    I have a region from inner radius to outer radius and from lower angle to upper angle (region is a piece of circular ring) - two edges are at constant radius and two are at constant angle. Do you have any equation for Stoke's theorem in polar coordinates.
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  4. #4
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    Re: Convert line integral to surface integral

    I solved this problem with divergence theorem.
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  5. #5
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    Re: Convert line integral to surface integral

    Really? The divergence theorem relates the integral over a closed surface to the integral over the volume enclosed by the surface. That is not what you were asking about before.
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  6. #6
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    Re: Convert line integral to surface integral

    I found equation on this page http://www.calpoly.edu/~dhartig/Page...olarCoords.pdf and I got what I wanted.
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