This is a problem from Chennai Mathematical Institute, CMI Entrance 2014 based on area of a region. Try to solve it.
Problem: Area of a region
. Find the area of A.
is a disc of radius 12 with center (0, 0).
Now notice that
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 =