If the area (in sq. units) of the region x , y : y 2 ≤ 4 x , x + y ≤ 1 , x ≥ 0 , y ≥ 0 is a 2 + b , then a - b is equal to

Step-by-step solution

The given equations are, y 2 = 4 x   &   x + y = 1 ⇒ y 2 = 4 1 - y ⇒ y 2 + 4 y - 4 = 0   ⇒ y = 2 2 - 2 ∴ Required Area = ∫ 0 2 2 - 2 1 - y - y 2 4 d x = y - y 2 2 - y 3 12 0 2 2 - 2 = 2 2 - 2 - 2 2 - 2 2 2 - 2 2 - 2 3 12 - 0 = 2 2 - 2 1 - 2 - 1 - 2 - 1 2 3 = - 10 3 + 8 2 3 ⇒ - 10 3 + 8 2 3 = a 2 + b   ⇒ a = 8 3 ,   b = - 10 3 ∴   a - b = 8 3 + 10 3 = 6