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.