Evaluate: `int_-100^100 Sgn(x-[x])dx`, where `[x]` denotes the integral part of `x`.

Show that: int_0^[[x]] (x-[x])dx=[[x]]/2 , where [x] denotes the integral part of x .

Evaluate int_(-2)^(4)x[x]dx where [.] denotes the greatest integer function.

int_0^1 [x^2-x+1]dx , where [x] denotes the integral part of x , is (A) 1 (B) 0 (C) 2 (D) none of these

Show that: (int_0^[x] [x]dx/(int_0^[x] {x}dx)=[x]-1 , where [x] denotes the integral part of x and {x}=x-[x] .

Evaluate int_(-3)^(5) e^({x})dx , where {.} denotes the fractional part functions.

Evaluate: int_0^(100)x-[x]dx where [dot] represents the greatest integer function).

int_0^2 x^3[1+cos((pix)/2)]dx , where [x] denotes the integral part of x , is equal to (A) 1/2 (B) 1/4 (C) 0 (D) none of these

The value of int_-1^10 sgn (x -[x])dx is equal to (where, [:] denotes the greatest integer function

Evaluate int_(0)^(2){x} d x , where {x} denotes the fractional part of x.

The value of int_0^100 [tan^-1 x]dx is, (where [*] denotes greatest integer function)