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]`.

If [x] denotes the integral part of [x] , find int_0^1[x]dx, .

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

If [x] denotes the integral part of x , find int_0^x[t+1]^3dt .

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

int_0^2{x}^([x])dx

Prove that int_0^1x e^x dx=1

If f(n)=(int_0^n[x]dx)/(int_0^n{x}dx) (where,[*] and {*} denotes greatest integer and fractional part of x and n in N). Then, the value of f(4) is...

Prove that int_0^x[t]dt=([x]([x]-1))/2+[x](x-[x]), 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

Evaluate (int_(0)^(n)[x]dx)/(int_(0)^(n){x}dx) (where [x] and {x} are integral and fractional parts of x respectively and n epsilon N ).