Calculating Area Inside Polar Curve: (-y/2)dx + (x/2)dy

[Tonyt88]

Homework Statement

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

r = 5 - 3sin(theta)

Homework Equations

The Attempt at a Solution

No idea where to begin.

 

[tim_lou]

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?

 

[Tonyt88]

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? :)