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Green's theorem- integral over an ellipse

  1. Nov 27, 2011 #1
    1. The problem statement, all variables and given/known data
    Use Green's theorem to find the integral ∫C (y^2dx+xdy) when C is the following curve (taken counterclockwise): the ellipse x^2/a^2 + y^2/b^2 =1.

    2. Relevant equations
    Green's theorem: ∫C Mdx+Ndy = ∫∫R (∂N/∂x-∂M/∂y)dA

    3. The attempt at a solution
    I tried parametrizing the ellipse as r(t)=(acost,bsint), but didn't know how to go on...

    I don't know how to solve the double integral over the ellipse ∫∫R (1-2y)dA.

  2. jcsd
  3. Nov 27, 2011 #2
    Begin with simpler things to get an idea: how to calculate the area of a circle of r=1?
    [tex]\int_{-1}^1\int_{???}^{???} dx dy[/tex]

    Replace the ???, then it should be clear for the ellipse.
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