`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_0^1 [x^2-x+1]dx , where [x] denotes the integral part of x , is (A) 1 (B) 0 (C) 2 (D) none of these

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

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

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

int_0^oo[3/(x^2+1)]dx, where [.] denotes the greatest integer function, is equal to (A) sqrt2 (B) sqrt2+1 (C) 3/sqrt2 (D) infinite

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

int_0^oo(x dx)/((1+x)(1+x^2)) is equal to (A) pi/4 (B) pi/2 (C) pi (D) none of these"

The period of function 2^({x})+sinpix+3^({x/2})+cos2pix (where {x} denotes the fractional part of (x) is 2 (b) 1 (c) 3 (d) none of these

The value of int_(-2)^1 [x[1+cos((pix)/2)]+1] dx, where [.] denotes greatest integer function is