Let A = x , y : y 2 ≤ 4 x , y - 2 x ≥ - 4 . The area of the region A in square units is

Step-by-step solution

Given, y 2 = 4 x       . . . 1 y = 2 x − 4 ⇒ 2 x = y + 4       . . . 2 Solving equations 1   &   2 , we get ⇒ y 2 = 2 y + 8 ⇒   y 2 - 2 y - 8 = 0 ⇒ y - 4 y + 2 = 0 ⇒ y = 4 ,   - 2 From equation 2 , If y = 4 then x = 4 and if y = - 2 then x = 1 . A = ∫ 0 4 4 x   d x - 1 2 × 2 × 4 + ∫ 0 1 4 x d x + 1 2 × 1 × 2 = 2 x 3 / 2 3 2 0 4 - 4 + 2 x 3 / 2 3 2 0 1 + 1 = 4 3 8 - 4 + 4 3 1 + 1 = 3 6 3 - 3