MathDB

integral inequality, condition 1≥int|f'(x)|^2 from 0 to 1

Source: SEEMOUS 2013 P3

June 8, 2021

calculusintegrationinequalities

Problem Statement

Find the maximum value of

\int^1_0|f'(x)|^2|f(x)|\frac1{\sqrt x}dx

over all continuously differentiable functions

f:[0,1]\to\mathbb R

with

f(0)=0

and

\int^1_0|f'(x)|^2dx\le1.