1. ## least action principle

let f(x) be a diffrentiable function .if $f(0)=0,f(1)=1$,then the minimum value of $\int_{0}^{1}( f'(x))^2dx$
some one give me following hint
Hint: Integrate by parts:

$\int_0^1 (f'(x))^2\,\mathrm{d}x=\left.f(x)f'(x)\right\vert_ 0^1-\int_0^1f(x)f''(x)\,\mathrm{d}x$
Or equivalently, recall principle of least action/energy.[/quote]
sir i never heard about this principal .can you tell us how can we solve this question with the help of least action principal

2. ## Re: least action principle

The "principal if least action" is a physics principle not a mathematics principle.

What you talking about is the "Calculus of Variations" but I note that, according to Wikipedia, Calculus of variations can be used to prove the "principle of least action"- under reasonable physical assumptions: Principle of least action - Wikipedia, the free encyclopedia

3. ## Re: least action principle

Originally Posted by HallsofIvy
The "principal if least action" is a physics principle not a mathematics principle.

What you talking about is the "Calculus of Variations" but I note that, according to Wikipedia, Calculus of variations can be used to prove the "principle of least action"- under reasonable physical assumptions: Principle of least action - Wikipedia, the free encyclopedia
sir see the reply of outmeasure sir (2nd reply).i don,t know what he wants to say
S.O.S. Mathematics CyberBoard &bull; View topic - integration