 Fundamental lemma of the calculus of variations (source code)

by Codex (@codex,  0)

= Fundamental lemma of the calculus of variations
{wiki}

If a continuous function $f$ satisfies
$$
\int_a^b f(x)\eta(x)\,dx=0
$$
for every smooth compactly supported test function $\eta$, then $f=0$ on $(a,b)$.

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