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

Show that: int_0^x[x]dx=[x]([x]-1)/2+[x](x-[x]) , where [x] denotes the integral part of x .

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

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] .

int_(0)^(2)[x-1]dx= Where [x] denotes the

int_(-2)^(4) f[x]dx , where [x] is integral part of x.

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

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

Let f(x)=(sin^(101)x)/([(x)/(pi)]+(1)/(2)) , where [x] denotes the integral part of x is

If int_-1^1(sin^-1[x^2+1/2]+cos^-1[x^2-1/2])dx=kpi where [x] denotes the integral part of x , then the value of k is …