If `f(x)=x+sinx ,` then find the value of `int_pi^(2pi)f^(-1)(x)dxdot`

If f:RrarrR defined by f(x)=sinx+x , then find the value of int_0^pi(f^-1(x))dx

Let a function f:R to R be defined as f (x) =x+ sin x. The value of int _(0) ^(2pi)f ^(-1)(x) dx will be:

if f(x)=x+sinx , then find (2)/(pi^(2)).int_(pi)^(2pi)(f^(-1)(x)+sinx)dx

If fx=x+sinx , then int_(pi)^(2pi)f^(-1)(x)dx is equal to

If f(x)=|(sin x+sin x 2x+sin3x,sin2x,sin3x),(3+4sinx,3,4sinx),(1+sinx,sinx,1)|, then the value of int_0^(pi/2) f(x) dx is

If f(x) = |(x,cos x,e^(x^(2))),(sin x,x^(2),sec x),(tan x,1,2)| , then the value of int_(-pi//2)^(pi//2) f(x) dx is equal to

If f(x) is a continuous function in [0,pi] such that f(0)=f(x)=0, then the value of int_(0)^(pi//2) {f(2x)-f''(2x)}sin x cos x dx is equal to

If f(x)=sin x-x, then int_(-2 pi)^(2 pi)|f^(-1)(x)|dx= (A) pi^(2)(B)2 pi^(2)(C)3 pi^(2)(D)4 pi^(2)

Let f(x)=(1-tan x)/(4x-pi),x!=(pi)/(4),x in[0,(pi)/(2)], If f(x) is continuous in [0,(pi)/(4)], then find the value of f((pi)/(4))

Let f(x)=(k cos x)/(pi-2x) if x!=(pi)/(2) and f(x=(pi)/(2)) if x=(pi)/(2) then find the value of k if lim_(x rarr(pi)/(2))f(x)=f((pi)/(2))