But WHY Does U-Substitution Work?

Feel free to pause the video if you need, I definitely went a bit fast in this video.

[NotGleSki]

Dude these are amazing like it’s so nice to have a short math YouTube video explaining something that I just fully skim past the though of in class

[ValidatingUsername]

For those trying to rationalize what is happening beyond what is illustrated, the metric tensor is literally transformed to map the function to something that you hopefully can solve algebraically.

[adityakhanna]

The first example touched on why u sub works but then failed to do expound it.
U sub is basically reparametrization. It controls how fast or slow you travel along your x, so u = 2x travels twice as fast

[Jqho-lv]

The guy in the thumbnail looks like Bach. I thought this was a tutorial on a baroque composing device LOL. Very interesting video by the way

[omerhamzasacan]

I just introduced to integration by parts and was confused on why it works. My teacher said that it was university thing to understand this and that he doesn't remember it anymore. Thanks for helping

[thebeardman]

This works better in with a multi variable example like going to polar coordinates then with the Jacobi matrix

[Eknoma]

I though you were going to show why it works, but then after the first two examples of when it works, the video just ended

[jmcsquared]

The way I have viewed it in one dimension is, since dx = (dx/du) du, it is just the chain rule applied to f(x)dx when you replace the variable x with the variable u.

In the same way that the ordinary chain rule works because it's basically canceling out terms in fractions, df/dx = (df/du) (du/dx), just with differential elements.

[eclipseninja]

Wow I have never thought about it like that amazing explanation 👍

[theimmux]

aing no way bros go to school and don't learn WHY sumn works

[meccamiles]

Very well articulated. Thanks for sharing.

[artemis_furrson]

My lecturer did perform a formal proof of integration by substitution, but I've never understood it geometrically until today.

[maximilianozetlenok]

Beautiful explanation! I finally understand what the hell was that. Like and subscribed. Greetings from Argentina!

[ihmejakki]

Really nice condensed information package!

[FunctionallyLiteratePerson]

Using the Jacobian for variable change works similarly but for multiple dimensions (tldr)

[jayjitsingha]

Earned a new sub mate...nicely explained

[toucansam]

What does it mean to be infinitesimally small and twice as large as something else that is infinitesimally small?

[navamoore]

Great video. Could you explain why integration by parts work?

[wavephasemusic]

Wow ! Amazing explanation! A+ … I got a degree without having a clue why this works 🤦‍♂️😵😑

[efloof]

I literally asked myself this a week ago on a run