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Green's Theorem

  1. Dec 10, 2006 #1
    1. The problem statement, all variables and given/known data

    Using the integral of (-y/2)dx + (x/2)dy
    Calculate the area inside the limacon with polar equation:

    r = 5 - 3sin(theta)


    2. Relevant equations



    3. The attempt at a solution

    No idea where to begin.
     
  2. jcsd
  3. Dec 11, 2006 #2
    notice that the divergence of the vector field that you are integrating over is 1. So, if you integrate 1 over the region of the limaçon, what can that integral be transformed into?
     
  4. Dec 11, 2006 #3
    I think I've got it:

    x = r cos(theta)
    y = r sin(theta)

    Solve for dx/d(theta) and dy(theta)

    Integrate from 0 to 2(pi) and that should go well? :)
     
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