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Fundamental Lemma of Calculus of Variations

If M is continuous and

int_a^bM(x)h(x)dx=0

for all infinitely differentiable h(x), then

M(x)=0

on the open interval (a,b).

See also

Calculus of Variations

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Cite this as:

Weisstein, Eric W. "Fundamental Lemma of Calculus of Variations." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FundamentalLemmaofCalculusofVariations.html

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