\documentclass[11pt]{scrartcl}
\usepackage{evan}

\begin{document}
\title{Twitch 165.2}
\subtitle{Evan Chen}
\author{Twitch Solves ISL}
\date{Episode 165}
\maketitle

\section*{Problem}
Let $f$ be a continuously differentiable function on $[0, \pi]$,
such that $f(0) = f(\pi) = 0$.
Prove that
\[ \int_0^\pi f'(x)^2 \odif x \ge \int_0^\pi f(x)^2 \odif x \]
with equality if and only $f(x) = c\sin x$ for some constant $c$.





\newpage

\section*{Solution}
The idea is to integrate
\[ \int_0^{\pi} \left( f'(x) - \cot x f(x) \right)^2 \odif x \ge 0. \]
Details to be added.

\end{document}
