Question

Find the area enclosed between the parabola y2 = x and the line x + y = 2

Answer 1

Given y = 2 – x and y2 = x

⇒ [2 – x]2 = x ⇒ 4 + x2 – 4x = x

⇒ x2 – 5x + 4 = 0 ⇒ (x – 4) (x – 1) = 0

⇒ x = 4 and x = 1

when x = 1 then y = 2 – 1 = 1 ⇒ (1,1)

when x = 4 then y = 2 – 4 = -2 ⇒ (4, -2)