The area bounded by the graph y = x -   3 , above the x -axis from x = - 2 to x = 3 is ( . denotes the greatest integer function)

Step-by-step solution

∴ Required area = ∫ - 2 3 x - 3 d x = ∫ - 2 - 1 x - 3 d x + ∫ - 1 0 x - 3 d x + ∫ 0 1 x - 3 d x + ∫ 1 2 x - 3 d x + ∫ 2 3 x - 3 d x = ∫ - 2 - 1 5 d x + ∫ - 1 0 4 . d x + ∫ 0 1 3 . d x + ∫ 1 2 2 . d x + ∫ 2 3 1 . d x = 5 1 + 4 1 + 3 1 + 2 1 + 1 1 = 15 s q . u n i t s .