The area (in sq . units ) of the region x , y : y 2 ≥ 2 x and x 2 + y 2 ≤ 4 x , x ≥ 0 , y ≥ 0 is

Step-by-step solution

y 2 ≥ 2 x   (Area outside the parabola) x 2 + y 2 ≤ 4 x (Area inside the circle) Finding point of intersection of the curves, we get, x 2 + y 2 = 4 x and y 2 = 2 x ⇒ x 2 + 2 x = 4 x ⇒ x 2 = 2 x ⇒ x = 0 ,   x = 2 If x = 0 , then y = 0 and if x = 2 , then y = ± 2 . Coordinates of A 0 ,   0 ,   B 2 ,   2 As x   ≥ 0   , y   ≥ 0 only area above x -axis would be considered. Hence, area = ∫ 0 2 4 x - x 2   d x -   2 &#16