So I'm trying to solve this problem stated like this:
Using Green's Theorem, find the area of the elipse defined by (where $a,b \gt 0$):
$\frac{x^2}{a^2} + \frac{y^2}{b^2} \leqq 1$
I'm having trouble doing this,
$\int_{FrD} \!F \cdot T = {\int\int}_D \left(\frac{df_2}{dx} - \frac{df_1}{dy}\right)$
Where $F$ is a vector field. My try at solving this was parametize the elipse as polar coords and doing $F$ as $F(x,y) = (1,1)$. Similiar to how to get the area. But I'm pretty sure that's not the correct way.