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I'm reading the section of Marion and Thornton devoted to basics on the Calculus of Variations, and came across this definition for the functional: $$J = \int f(y(x), y'(x);x) dx$$ implying that $f$ depends on both $y(x)$ and $y'(x)$.

I'm confused as to why $f$ depends explicitly on both $y$ and $y'$, since $y'$ is already specified by the choice of $y$.

Any help/explanation would be appreciated!

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marked as duplicate by Qmechanic Nov 14 '18 at 5:42

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