The area (in sq. units) of the region described by x , y : y 2 ≤ 2 x and y ≥ 4 x - 1 is

Step-by-step solution

Let us find the points intersections of y 2 = 2 x and y = 4 x - 1 ⇒ 4 x - 1 2 = 2 x ⇒ 1 6 x 2 - 1 0 x + 1 = 0 ⇒ 8 x - 1 2 x - 1 = 0 ⇒   x = 1 2 , 1 8 x = 1 2  ⇒ y = 4 1 2 - 1 = 1   ⇒ A 1 2 , 1 x = 1 8  ⇒ y = 4 1 8 - 1 = - 1 2 ⇒ B 1 8 , - 1 2 A 1 = ∫ 0 1 8 2 x d x   +   1 2 × 1 8 × 1 2 A 1 = 2 x 3 2 3 2 0 1 8   +   1 32 A 1 = 1 24   +   1 32   sq . units A 2 = ∫ 0 1 2 2 x d x   -   1