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
$\displaystyle \frac{1}{2} \oint \limits_c -y \,dx + x\,dy = \iint \limits_R dA$ with the latter the area of the region $\displaystyle R$.
Then let $\displaystyle x = a \cos \theta $ and $\displaystyle y = b \sin \theta $ and compute the line integral.