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Fundamental Lemma of Calculus of Variations

If

\begin{displaymath}
\int^b_a M(x)h(x)\,dx = 0
\end{displaymath}

$\forall\ h(x)$ with Continuous second Partial Derivatives, then

\begin{displaymath}
M(x) = 0
\end{displaymath}

on the Open Interval $(a,b)$.




© 1996-9 Eric W. Weisstein
1999-05-26