Green's theorem- integral over an ellipse

[aylwin]

Homework Statement

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.

Homework Equations

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

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.

 

[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.