# Green's theorem- integral over an ellipse

1. Nov 27, 2011

### aylwin

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.

Thanks.

2. Nov 27, 2011

### Quinzio

Begin with simpler things to get an idea: how to calculate the area of a circle of r=1?
$$\int_{-1}^1\int_{???}^{???} dx dy$$

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