The area bounded by curves (x-1)²+y²=1 and x²+y²=1 is

Step-by-step solution

Given circles are x²+y²=1 (i) and (x-1)²+y²=1 (ii) Centre of (i) is O (0,0) and radius =1 Both these circle are symmetrical about x -axis solving (i) and (ii), we get, -2 x+1=0 x= 1 2 array l then y²=1- ( 1 2 )²=34 y= 3 2 array The points of intersection are P ( 1 2 , 3 2 ) and Q ( 1 2 ,- 3 2 ) It is clear from the figure that the shaded portion in region whose area is required. Required area = area OQAPO =2 area of the region OLAP =2 ( area of the region O L P O+ area of L A P L ) =2 [ ₀^ 1 2 1-(x-1)² d x+ _ 1 2 ¹