1. ## green's theorem

using green's theorem, verify that the area enclosed by the ellipse (x^2)/(a^2)+ (y^2)/(b^2)=1 is given by a*b*pi

how do i do this? i've tried many times and don't even get the answer a*b*pi any help would be great thanks

2. Originally Posted by calc626
using green's theorem, verify that the area enclosed by the ellipse (x^2)/(a^2)+ (y^2)/(b^2)=1 is given by a*b*pi

how do i do this? i've tried many times and don't even get the answer a*b*pi any help would be great thanks
Via Green's theorem

$\frac{1}{2} \oint \limits_c -y \,dx + x\,dy = \iint \limits_R dA$ with the latter the area of the region $R$.

Then let $x = a \cos \theta$ and $y = b \sin \theta$ and compute the line integral.

3. hmm that's what i've been trying but have not been getting the right answer somehow. is the integral from 0 to 2pi?

4. Originally Posted by calc626
hmm that's what i've been trying but have not been getting the right answer somehow. is the integral from 0 to 2pi?
Yes. If you show us some of your details maybe we can help.