- #1

Niles

- 1,866

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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] ->

**R**be continuous 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 in

**R**

^{k}?