A function satisfying `int_0^1f(tx)dt=nf(x)`, where `x>0` is

Let f:R ->(0,oo) be a real valued function satisfying int_0^x tf(x-t) dt =e^(2x)-1 then find f(x) ?

Let f:(0,oo)vec(0,oo) be a differentiable function satisfying, xint_0^x(1-t)f(t)dt=int_0^x tf(t)dtx in R^+a n df(1)=1. Determine f(x)dot

Let f:(0,oo)vec(0,oo) be a differentiable function satisfying, xint_0^x(1-t)f(t)dt=int_0^x tf(t)dtx in R^+a n df(1)=1. Determine f(x)dot

Let f(x) is differentiable function satisfying 2int_(1)^(2)f(tx) dt = x+2, AA x in R Then int_(1)^(2)(8f(8x)-f(x)-21x) dx equal to

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 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

Consider a function f: [0, 1] -> R satisfying int_0 ^1 (f(x)(x-f(x))dx = 1/12 , then, f'(1) is k where [1/k] is

Let f(x) be a function satisfying f'(x)=f(x) with f(0) =1 and g(x) be a function that satisfies f(x) + g(x) = x^2 . Then the value of the integral int_0^1f(x) g(x) dx , is

Let f be a continuous function satisfying the equation int_(0)^(x)f(t)dt+int_(0)^(x)tf(x-t)dt=e^(-x)-1 , then find the value of e^(9)f(9) is equal to…………………..

Let f(x) and phi(x) are two continuous function on R satisfying phi(x)=int_(a)^(x)f(t)dt, a!=0 and another continuous function g(x) satisfying g(x+alpha)+g(x)=0AA x epsilonR, alpha gt0 , and int_(b)^(2k)g(t)dt is independent of b If f(x) is an odd function, then