`int_- 1^1(sin^(- 1)[x+3/4])dx=pi/k`, then k is where [ ] denotes GIF)

int_(-1)^(1)(sin^(-1)[x+(3)/(4)])dx=(pi)/(k), then k is where [1] denotes GIF )

If int_-1^1(sin^-1[x^2+1/2]+cos^-1[x^2-1/2])dx=kpi where [x] denotes the integral part of x , then the value of k is …

For x in(0, (pi)/(2)) If int(tan x sqrt(sec x)(1+cos^(2)x))/(sqrt(cos x+sin^(2)x))dx=2sqrt(f(x)+1)+c and f((pi)/(3))=(3)/(2) then [f((pi)/(4))] = ( where [.] denotes G.I.F )

The value of int_(-1)^(1)sin^(-1)[x^(2)+(1)/(2)]dx+int_(-1)^(1) cos^(-1)[x^(2)-(1)/(2)]dx , where [.] denotes the greatest integer function , is

If f(x)=sin^(-1)x and lim_(xto1//2+)f(3x-4x^3)=a-3lim_(xto1//2+)f(x) , then [a] is equal to {where [] denotes G.I.F}

The value of int_(-2)^(2)(sin^(2)x)/([(x)/(pi)]+(1)/(2))dx, where [*] denotes greatest integer function,is

If I_(1)=int_(0)^((pi)/(2))e^(sinx)(1+x cos x)dx and I_(2)=int_(0)^((pi)/(2))e^(cosx)(1-x sin x)dx, then [(I_(1))/(I_(2))] is equal to (where [x] denotes the greatest integer less than or equal to x)

Consider qquad I_(K)=int_(0)^(K)[Tan^(-1)x]dx , where [.] denotes GIF function

The period of the function f(x)=4sin^(4)((4x-3 pi)/(6 pi^(2)))+2cos((4x-3 pi)/(3 pi^(2))) is k pi^(3) then the value of [1/k] (where [ ] denote the G.I.F )