Find the area of the region enclosed between the two circles `x^2 + y^2 =1` and `(x-1)^2 + y^2 = 1`

Explanation

`(x^2+y^2)=1` is a circle with is its centre at (0,0) and radius =1 unit

And `(x-1)^2 +y^2=1` is a circle with its centre at (1,0) and radius =1 unit.
The given equations are
`(x^2 +y^)=1`
and `(x-1)^2 +y^2=1`
Using (i) in (ii) ,we get 1-2x =0 `rArr x= 1/2`
Putting `x=1/2` in (i) ,we get `y=pm (sqrt(3))/(2)`
So the two circles interset at A `(1/2,(sqrt(3))/(2)) " and B" (1/2 ,(-sqrt(3))/2)`
Required area = area AOBCA
= 2 (area AOCA) =2 (area ODAO+ area DCAD )
`2{underset(0)overset(1//2)int sqrt(1-(x-1)^2) dx + underset(1//2)overset(1)int sqrt(1=x^2)}`