Evaluate: `int_0^x[cost]dt` where `x in (2npi,4n+1pi/2),n in N ,a n d[dot]` 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 ...

int_(0)^(x)[sin t]dt, where x in(2n pi,(2n+1)pi),n in N, and [.] denotes the greatest integer function is equal to -n pi(b)-(n+1)pi2n pi(d)-(2n+1)pi

Evaluate: int_(0)^(2 pi)[sin x]dx, 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

int_(-n)^(n)(-1)^([x])backslash dx when n in N= in all of these [.] denotes the greatest integer function

lim_(x->0) (lnx^n-[x])/[x], n in N where [x] denotes the greatest integer is

int_(0)^(2pi)[|sin x|+|cos x|]dx , where [.] denotes the greatest integer function, is equal to :

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

Evaluate int_(0)^(a)[x^(n)]dx, (where,[*] denotes the greatest integer function).

lim_(xrarr oo) (logx^n-[x])/([x]) where n in N and [.] denotes the greatest integer function, is