`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_0^9{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, .

The value of int_(-2)^1[x[1+cos((pix)/2)]+1]dx , where [.] denotes the greatest integer function, is (a)1 (b) 1//2 (c) 2 (d) none of these

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

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

lim_(x->0) {(1+x)^(2/x)} (where {.} denotes the fractional part of x (a) e^2−7 (b) e^2−8 (c) e^2−6 (d) none of these

int_(-1)^2[([x])/(1+x^2)]dx ,w h e r e[dot] denotes the greater integer function, is equal to (a) -2 (b) -1 (c) 0 (d) none of these

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 …