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Homework Help: Line integral

  1. May 10, 2009 #1
    Hello all,

    I am trying to solve a line integral:

    Find the value of \int -2y dx + x^2 dy over the circle x^2 + y^2 = 9

    as you can see, this is a line integral, and I am trying to figure a quick way how it should be solved.
    I thought of converting coordinates to (sint,cost) which will end up as a trigonometric function which needs to be integrated, but I believe there is a much easier way which I am not sure about.

    Also, I am not sure what is the notation f(y) dx + g(x) dy stands for.
    Is it the same as [f(y) - i g(x)] dz?

    Thanks for any help.
  2. jcsd
  3. May 12, 2009 #2

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    Convert it to a area integral using Green's theorem, which relates a double integral over a region to a line integral over the boundary of the region. The integration becomes very easy.

    f(x)dx + g(y)dy is not the same as [f(y) - i g(x)] dz. The latter is a complex function whereas the former is not.
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