Show that: `int_0^x[x]dx=[x]([x]-1)/2+[x](x-[x])`, 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] .

Prove that int_(0)^(x) [x]dx=[x]([x]-1)/(2)+[x] (x-[x]) , where [.] denotes the greatest integer function

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

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

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

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

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

The functions f and g are given by f(x)=(x) the fractional part of x and g(x)=(1)/(2)sin[x]pi where Ix] denotes the integral part of x, then range of gof(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 …