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)