`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`

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

lim_(n->oo)(n(2n+1)^2)/((n+2)(n^2+3n-1)) is equal to (a)0 (b) 2 (c) 4 (d) oo

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

Ifg(x)=int_0^x(|sint|+|cost|)dt ,t h e ng(x+(pin)/2) is equal to, where n in N , g(x)+g(pi) (b) g(x)+g((npi)/(n2)) g(x)+g(pi/2) (d) none of these

If y=(1+t a n A)(1-t a n B), where A-B=pi/4, then (y+1)^(y+1) is equal to 9 (b) 4 (c) 27 (d) 81

If f(x)=sqrt(1-sin2x) , then f^(prime)(x) is equal to (a) -(cosx+sinx),forx in (pi/4,pi/2) (b) cosx+sinx ,forx in (0,pi/4) (c) -(cosx+sinx),forx in (0,pi/4) (d) cosx-sinx ,forx in (pi/4,pi/2)

"If " int x e^(x) cosx dx=ae^(x)(b(1-x)sinx+cx cosx)+d, then

If 4sin^4x+cos^4x=1 ,then x is equal to (n in Z) (a) npi (b) npi+-sin^(-1)sqrt(2/5) (c) (2npi)/3 (d) 2npi+-pi/4

Evaluate int(dx)/(5+4cosx)= a tan^(-1) (b t a n (x/2))+C , then

If y=cos^(-1)(cosx),t h e n(dy)/(dx) at x= (5pi)/4 is equal to (a)1 (b)-1 (c)0 (d)4