`int_0^x[sint]dt ,w h e r ex in (2npi,(2n+1)pi),n in N ,a n d[dot]` denotes the greatest integer function is equal to `-npi` (b) `-(n+1)pi` `2npi` (d) `-(2n+1)pi`

Evaluate: int_0^(2pi)[sinx]dx ,w h e r e[x] 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_(-pi/2)^(2pi)[cot^(-1)x]dx ,where [dot] denotes the greatest integer function.

Evaluate lim_(n->oo) [sum_(r=1)^n(1/2) ^r] , where [.] denotes the greatest integer function.

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

int_0^x|sint|dt , where x in (2npi,(2n+1)pi) , ninN ,is equal to (A) 4n-cosx (B) 4n-sinx (C) 4 n+1-cosx (D) 4n-1-cosx

The value of int_0^x[cost]dt ,x in [(4n+1)pi/2,(4n+3)pi/2]a n dn in N , is equal to where [.] represents greatest integer function. pi/2(2n-1)-2x pi/2(2n-1)+x pi/2(2n+1)-x (d) pi/2(2n+1)+x

Let R=(5sqrt(5)+11)^(2n+1)a n df=R-[R]w h e r e[] denotes the greatest integer function, prove that Rf=4^(2n+1)

If p=(8+3sqrt(7))^n a n df=p-[p],w h e r e[dot] denotes the greatest integer function, then the value of p(1-f) is equal to a. 1 b. 2 c. 2^n d. 2^(2n)

lim_(xto0^(+)) (sum_(r=1)^(2n+1)[x^(r)]+(n+1))/(1+[x]+|x|+2x), where ninN and [.] denotes the greatest integer function, equals