Using the Euler-Lagrange Equation to Show the Shortest Distance on a Plane is a Line

In this video, I show how one can use the Euler-Lagrange equations from the Calculus of Variations to show that the shortest distance between 2 points on a plane is a straight line.

[@reddykiranrsr]

Like a thriller movie .. Lot of suspense but finally got answer. Thank you and you made my life easy.

[@dejremi8190]

Wouaw Never had i thought that this result was so formally proved thanks for the video!

[@KyleKabasares_PhD]

Dej Rémi You’re welcome!

[@erlefurre3966]

you are a amazing! thank you for making it easy!

[@asymptoticspatula]

Very helpful. Thank you.

[@maikopskoy]

Thanks that was so well explained

[@callme_lyds]

This really helped me! Thank you.

[@KyleKabasares_PhD]

I'm glad!

[@FrederickHyltonDei]

Thanks for your effort to teach us in a way that is understandable

[@gamingarghya7436]

Thanks, thats helpful

[@njabulomahlalela2912]

that was awesome❤

[@amikaokram5523]

Thnks

[@ericssonvancolborn726]

At 8:20, would you not also have to multiply by y ' ' (x) because of the chain rule?

[@jacobruiz6206]

I believe so

[@tonyjing7305]

You don't need to, because you are differentiating with respect to [y'(x)]. Even if you try to use the chain rule again, you'd multiply by derivative of y'(x) with respect to y'(x), but that is just 1 so you don't have to write it. It would be different if you were differentiating with respect to x.