`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)^(x)[cos t]dt where x in(2n pi,4n+1(pi)/(2)),n in N, and.] denotes the greatest integer function.

If f(n)=int_(0)^(x)[cos t]dt, where x in(2n pi,2n pi+(pi)/(2));n in N and [*] denotes the greatest integer function.Then, the value of f((1)/(pi))| is ...

f(x)=lim_(n rarr oo)sin^(2n)(pi x)+[x+(1)/(2)], where [.] denotes the greatest integer function,is

int _(0) ^(2npi) (|sin x | - [|(sin x )/(2) | ]) dx is equal to (where [**] denotes the greatest integer function)

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

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)

int_(0)^(x)|sin t|dt, where x in(2n pi,(2n+1)pi)n in N, is equal to (A)4n-cos x(B)4n-sin x(C)4n+1-cos x(D)4n-1-cos x

int_(-pi)^( pi)|x sin[x^(2)-pi}|dx=sum_(r=0)^(n)a_(r)sin r where Il denote the greatest integer function and a_(r),r=0,1,2,...n are real constants then n is equal to