The area of the region bounded by parabola y² = x and the straight line 2y = x is

Given;

Parabola y² = x and the straight line 2y = x

By substituting for x;

⇒ y² = 2y

⇒ y (y − 2) = 0

∴ y = 0, 2.

∴ x = 2y = 0, 4.

Required area