The area of the region (in sq. units), enclosed by the circle x 2 + y 2 = 2 which is not common to the region bounded by the parabola y 2 = x and the straight line y = x , is

Step-by-step solution

Required area = 2 π - ∫ 0 1 x - x d x = 2 π - 2 x 3 2 3 - x 2 2 0 1 = 2 π - 2 3 - 1 2 = 2 π - 1 6 = 12 π - 1 6   sq . units