If [x] is the greatest integer not exceeding x , then _ -0.5 ^ 1.5 x^2[x] d x=

Step-by-step solution

aligned & _ -0.5 ^ 1.5 x^2[x] d x= _ -0.5 ^0 x^2(-1) d x+ ₀^1 x^2(0) d x+ ₁^ 1.5 x^2(1) d x & =- 1 3 [x^3 ]_ - 1 2 ^0+ 1 3 [x^3 ]₁^ 3 / 2 = 3 4 aligned