The area (in sq. units) of the region x ∈ R : x ≥ 0 , y ≥ 0 , y ≥ x - 2 and y ≤ x is

Step-by-step solution

y = x x = x - 2 ( x ) 2 - ( x ) - 2 = 0 ( x - 2 ) ( x + 1 ) = 0 x = 2 ⇒ x = 4 Therefore, the area of the region is ∫ 0 4 x d x - Area of ∆ A B C = 2 3 x 3 / 2 0 4 - 1 2 × 2 × 2 = 2 3 × 4 3 / 2 - 2 = 16 3 - 2 = 10 3 sq . unit