Hence if a point (x, y) is in A then (-x, -y) is not in A.
Similarly if there is a point (x, y) not in A then we get a corresponding point (-x, -y) in A.

Therefore we have a bijection between points in A and not in A.

Thus area of A is exactly half the area of the disc =

This can in fact be generalised to any odd function f(x). f(ax+by) divides the area of the disc in half if f is odd.