How to Visualize Minimizing Definite Integrals and Understand Stationary Points?

[richardlhp]

Calculus of variations (HELP!)

Hi all! Just a question...

How should I visualise geometrically the minimising of definite integrals, and what is the significance of finding stationary points of definite integrals? (Can someone provide me with an intuitive explanation?)

Thanks so much!

 

[mathman]

Assuming you mean the definite integral has a parameter, work with the expression as a function of the parameter and then apply elementary calculus methods. Being a definite integral is not particularly relevant.

 

[stevenb]

He probably means variations of functions and not parameters.

Intuitively, it's similar to minimization in multivariable calculus, but with an infinite number of dimensions.

OK, the mathematicians should be sufficiently stunned that I have a few seconds to duck for cover.

 

[richardlhp]

Thanks so much!