Mean of Differentiable Function (Jee Mains)

Continuity and Differentiability

Hard

Mean of Differentiable Function

Let f be a twice differentiable non-negative function such that (f(x))² = 25 + $\int\limits_0^x {\;\left( {{{(f(t))}^2} + {{(f'(t))}^2}} \right)}$ dt. Then the mean of f(log_e(1)), f(log_e(2)), ... , f(log_e(625)) is equal to ________ .

Ask about this question