Find the area of the region bounded by the curve y2 = 2x and x2+y2 = 4x.

Find the area of the region bounded by the curve y2 = 2x and x2+y2 = 4x.

We have,y,2, = 2x and x,2, + y,2 ,= 4x,y,2, = 2x is parabola opening to the right of positive direction x-axis ,x,2,+y,2, = 4x,⇒ (x-2),2 ,+ y,2, = 4, which is circle having centre at (2,0) and radius'2',Solving the curves we get, ,x,2,+2x=4x,⇒ x,2,-2x=0,⇒ x=0,2,When x = 0,y=0 and when x=2, y±2 ,Thus points of intersection are (0,0),(2,2) and (2,-2),The graph  is as shown in the following figure.,