`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

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

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

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

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

int _(0)^(2) x ^(3) [1+ cos ""(pix)/(2)] dx is (where [**] denotes the greatest integer function)

The value of int_(1)^(oo)[cos ec^(-1)x]dx .(where [.] denotes greatest integer function),is equal to (A) cos ec1-1(B)1(C)1-sin1(D) none of these

Show that: int_0^x[x]dx=[x]([x]-1)/2+[x](x-[x]) , where [x] denotes the integral part of x .

int_(-1)^(2)[([x])/(1+x^(2))]dx, where [.] denotes the greater integer function,is equal to -2(b)-1zero (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