The area (in square units) bounded by the curves y = x , 2 y - x + 3 = 0 , X -axis and lying in the first quadrant is

Step-by-step solution

First draw the given curves and represent the required area. Eliminate x to find point of intersection of y = x and 2 y - x + 3 = 0 ⇒ 2 y - y 2 + 3 = 0 ⇒ y 2 - 2 y - 3 = 0 ⇒ y - 3 y + 1 = 0 ⇒ y = 3 , - 1 ∴ Required area A = ∫ 0 9 x d x - 1 2 × 6 × 3 A = x 3 2 3 2   0 9 - 9 ∴ A = - 9 Hence, area is 9   sq .   units