Let `f` be a differentiable function satisfying `int_(0)^(f(x))f^(-1)(t)dt-int_(0)^(x)(cost-f(t)dt=0` and `f((pi)/2)=2/(pi)`
The value of `int_(0)^(pi//2) f(x)dx` lies in the interval

Let f be a differentiable function satisfying int_(0)^(f(x))f^(-1)(t)dt-int_(0)^(x)(cost-f(t)dt=0 and f((pi)/2)=2/(pi) The value of lim_(x to 0)(cosx)/(f(x)) is equal to where [.] denotes greatest integer function

Let f be a differentiabel function satisfying int_(1)^(f(x))f^(-1)(t)dt=(1)/(3)(x^((3)/(2))-8)AA x>0 and f(1)=0 Then the value of f(9) is

Let f be a differentiabel function satisfying int_(1)^(f(x))f^(-1)(t)dt=(1)/(3)(x^((3)/(2))-8)AA x>0 and f(1)=0, Then the value of f(9) is

Let f(x) be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt then int_(0)^(1)f(x)dx=

f(x)=x^(3)+1-2x int_(0)^(x)g(t)dt and g(x)=x-int_(0)^(1)f(t)dt. Then yhe value of int_(0)^(1)f(t)dt lies in the interval

Let f:(0,oo)rarr(0,oo) be a differentiable function satisfying,x int_(x)^(x)(1-t)f(t)dt=int_(0)^(x)tf(t)dtx in R^(+) and f(1)=1 Determine f(x)

Let f(x) be a differentiable function satisfying f(x)=int_(0)^(x)e^((2tx-t^(2)))cos(x-t)dt , then find the value of f''(0) .

if f be a differentiable function such that f(x) =x^(2)int_(0)^(x)e^(-t)f(x-t). dt. Then f(x) =

f(x)=sinx+int_(-pi//2)^(pi//2)(sinx+tcosx)f(t)dt The value of int_(0)^(pi//2) f(x)dx is

If int_(0)^(x)f(t)dt=x^(2)+int_(x)^(1)t^(2)f(t)dt, then f'((1)/(2)) is