find area of ellipse by green theorem

**szpengchao** · April 30th 2008, 05:03 AM

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

**ThePerfectHacker** · April 30th 2008, 07:05 AM

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.

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