The range of the function `f(x)=int_(-1)^1(sinxdt)/((1-2tcosx+t^2)i s` (a)`[-pi/2,pi/2]` (b) `[0,pi]` (c)`{0,pi}` (d) `{-pi/2,pi/2}`

The range of the function f(x)=int_(-1)^(1)(sinxdt)/(1+2tcosx+t^(2)) is

[" The range of the function "f(x)=sin^(-1)((sqrt(1+x^(4)))/(1+5x^(10)))" is "],[[[-(pi)/(2)*(pi)/(2)]],[0[(pi)/(3)*(pi)/(2))],[0(0,(pi)/(2)]]]

The Range of the function y=((cos^(-1)(3x-1))/(pi)+1)^(2)(1)[1,4](2)[0,pi](3)[1,pi](4)[0,pi^(2)]

Range of function f(x)=arccot(2x-x^(2)) is [(pi)/(4),(3 pi)/(3)](b)[0,(pi)/(4)][0,(pi)/(2)] (d) [(pi)/(4),pi]

The range of function f(x)=cot^(-1)x+sec^(-1)x+ cosec^(-1)x is (A) [(pi)/(2), pi)uu(pi, (3 pi)/(2)] (B) ((pi)/(2), (3 pi)/(4)] uu [(5 pi)/(4), (3 pi)/(2)) (C) ((pi)/(2), pi)uu(pi ,(3 pi)/(2)) (D) ((pi)/(2), (3 pi)/(2))

The largest interval lying in (-pi/2,pi/2) for which the function [f(x)=4^-x^2+cos^(-1)(x/2-1)+log(cosx)] is defined, is (1) [0,pi] (2) (-pi/2,pi/2) (3) [-pi/4,pi/2) (4) [0,pi/2)

The range of f(x)=sin^(-1)(sqrt(x^(2)+x+1)) is (0,(pi)/(2))(b)(0,(pi)/(3))(c)((pi)/(3),(pi)/(2)) (d) [(pi)/(6),(pi)/(3)]

The function f(x)=tan^(-1)(sin x+cos x) is an increasing function in (-(pi)/(2),(pi)/(4))(b)(0,(pi)/(2))(-(pi)/(2),(pi)/(2))(d)((pi)/(4),(pi)/(2))

Range of tan^(-1)((2x)/(1+x^(2))) is (a) [-(pi)/(4),(pi)/(4)] (b) (-(pi)/(2),(pi)/(2))(c)(-(pi)/(2),(pi)/(4)) (d) [(pi)/(4),(pi)/(2)]

int_-1^1 sin^-1(x/(1+x^2))dx= (A) pi/4 (B) pi/2 (C) pi (D) 0