Green's Theorem

  • Thread starter Tonyt88
  • Start date
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.
 
683
1
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?
 
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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