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

Evaluate: int_0^2[x^2-x+1]dx ,w h e r e[dot] denotos the greatest integer function.

Evaluate: int_(-5)^5x^2[x+1/2]dx(w h e r e[dot] denotes the greatest integer function).

("lim")_(xvec1)(xsin(x-[x]))/(x-1),w h e r e[dot] denotes the greatest integer function is equal to (a) 0 (b) -1 (c) not exist (d) none of these

Evaluate: int_1^(e^6)[(logx)/3]dx ,w h e r e[dot] denotes the greatest integer function.

int_0^x(2^t)/(2^([t]))dt ,w h e r e[dot] denotes the greatest integer function and x in R^+ , is equal to

Prove that int_0^oo[cot^(-1)x]dx ,w h e r e[dot] denotes the greatest integer function.

Evaluate: int_0^(2pi)[sinx]dx ,w h e r e[x] denotes the greatest integer function.

The integral int_0^(1. 5)[x^2]dx ,w h e r e[dot] denotoes the greatest integer function, equals ...........

Prove that int_(-pi/2)^(2pi)[cot^(-1)x]dx ,where [dot] denotes the greatest integer function.

T h ev a l u eofint_(-2)^1[x[1+cos((pix)/2)]+1]dx , where [.] denotes the greatest integer function, is 1 (b) 1//2 (c) 2 (d) none of these