`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

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

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

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

int_0^9{sqrt(x)}dx , where {x} denotes the fractional part of x , is 5 (b) 6 (c) 4 (d) 3

int_0^9{sqrt(x)}dx , where {x} denotes the fractional part of x , is 5 (b) 6 (c) 4 (d) 3

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_0^1[x]dx, .

int_(-1)^(1){x^(2)+x-3}dx, where {x} denotes thefractional part of x, is equal to

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