# Math Help - area of overlapping circles with equal radius using intergration.

1. ## area of overlapping circles with equal radius using intergration.

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)

2. ## Complicated

Define $a=r\cos\beta, b=r, d=r+p, c=\frac{p+\sqrt{p^2+(r^2-p^2)(1+\tan^2\beta)}}{1+\tan^2\beta}$

Define $y_0=\sqrt{r^2-x^2}, y_1=\sqrt{r^2-(x-p)^2}, y_2=x\tan\beta$

$A=\int_a^c y_2 dx - \int_a^b y_0 dx + \int_c^d y_1 dx$

This is assuming $\beta$ is the angle off the x-axis, and A is the area bounded in the region you specified, above the x-axis. If the bottom part is different, choose the different value of $\beta$ and evaluate again.

*I can draw a picture and walk you through where all of this comes from, if you want. I hope you don't seek A explicitly.