# Evaluating integral of Green's theorem

Applying Green's theorem, I've obtained a double integral of $$\iint_c 4ye^{-x^2 - y^2} \cos (2xy) dx dy = 0$$ along the curve $x^2 + y^2 \le R^2$.

Why is it equal to $0$?

The explanation I got was because "the integral in anti-symmetric (odd) in $y$ and the area of integration is symmetric in $y$."

Will anyone please tell me what does the above sentence means exactly? Thanks.

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"Antisymmetric in $y$" means that $f(x,-y)=-f(x,y)$. Imagine cutting up the region of integration into a "left" and "right" portion. Note that the integral on the "left" is precisely the negative of the integral on the "right" due to the oddness. –  Ｊ. Ｍ. Nov 6 '11 at 4:38
You might be interested in this thread. –  Ｊ. Ｍ. Nov 6 '11 at 4:43