# Thread: find area of ellipse by green theorem

1. ## find area of ellipse by green theorem

1. By greens theorem, find an expression for the area of the region R, and apply this to evaluate the area of the ellipse bounded by the curve.

x= a cos theta, y=b sin theta

2. Originally Posted by szpengchao
1. By greens theorem, find an expression for the area of the region R, and apply this to evaluate the area of the ellipse bounded by the curve.

x= a cos theta, y=b sin theta
Parametrize the curve as $\bold{g}(\theta) = (g_1(\theta),g_2(\theta))$ for $0\leq \theta \leq 2\pi$ where $g_1(\theta)=a\cos \theta$ and $g_2(\theta) = b\sin \theta$.

Then, $\iint_R 1 dA=\frac{1}{2}\int_C -ydx + xdy$.

Now evaluate that line integral to get the answer.