MathDB
ICMC 2018/19 Round 1, Problem 5

Source: Imperial College Mathematics Competition 2018/19 - Round 1

August 7, 2020
college contests

Problem Statement

For continuously differentiable function f:[0,1]→Rf : [0, 1] \to\mathbb{R} with f(1/2)=0f (1/2) = 0, show that
(∫01f(x)dx)2≤14∫01(f′(x))2dx\left(\int_0^1 f(x)\mathrm{d}x\right)^2\leq \frac{1}{4}\int_0^1\left(f'(x)\right)^2\mathrm{d}x
Back to ProblemsView on AoPS