Let where and .
Green's theorem says
However, if you had then:
Because the area of the ellipse is given by .
where
C is the ellipse x^2/a^2 + y^2/b^2 = 1
a,b>0
So basically I get upto II(-2)dxdy, with the elipse as limits, then converting to polar co-ordinates i'm unsure on the limits, but I have a vague idea it is sqrt(ab), can anyone confirm this? Would be appreciated, also can anyone tell me the best way be able to post all the different mathematical symbols