`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[cost]dt where x in (2npi,(4n+1pi/2),n in N ,a n d[dot] denotes the greatest integer function.

int_0^x[cost]dt ,w h e r ex in (2npi,2npi+pi/2),n in N ,a n d[dot] denotes the greatest integer function . then the value of f(1/pi) is

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)

Prove that int_0^oo[n e^(-x)]dx=1n((n^n)/(n !)),w h e r en is a natural number greater than 1 and [.] denotes the greatest integer function..

If sin^3theta+sinthetacos^2theta=1,t h e ntheta is equal to (n in Z) (a) 2npi (b) 2npi+pi/2 (c) 2npi-pi/2 (d) npi

The function f(x)=tanx is discontinuous on the set {npi; n in Z} (b) {2npin in Z} {(2n+1)pi/2: n in Z} (d) {(npi)/2: n in Z}

The solution of the equation sin^3x+sinxcosx+cos^3x=1 is (n∈N) (a) 2npi (b) (4n+1)pi/2 (c) (2n+1)pi (d) None of these