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In my notes I wrote down from the blackboard, I wrote

[Fundemental Lemma of the Calculus of Variations] Let f : [a,b] ->Rbe continous and suppose that

[tex]

\int_a^b f(t)h(t)dt = 0

[/tex]

for all [itex]h\in C_{0,0}^1([a,b], R)[/itex], where [itex]C_{0,0}^1([a,b], R)[/itex] is the space of C^{1}parametrized curves O : [a,b] -> R that start and end in 0.

I suspect that I missed some^{k}'s when writing this down from the blackboard. Am I correct when I say that this also works if we are inR^{k}?

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# Fundemental Lemma of the Calculus of Variations

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