Given two identical circles of radius 'r':

1. If the centers of the circles are less than 'r'(p) apart, what is the non-intersection area?

(using intergration : variables- p (distance between two centers of the circle); ß (angle of intersection)

2. what if ß increase or decrease ?

To make my question clear, look into the attached picture below.

( hatch area to be calculated)