can you evaluate this crazy integral??

[@gael8828]

Wait, after the t substitution, the argument inside the arctan is wrong. Should be (t^2-4)/2sqrt(2)

[@jzim5426]

I think so too. The expression for dx is wrong also: The factor 4 should be 1. But this did not change the result because it was canceled out by a missing factor of 4 when substituting the denominator.

[@cyanide7833]

yep, due to this i thought there was no way that the final answer could be correct, wolfram alpha approximated the integral to 2.26 however the value to (pi)ln(1+sqrt(2)) is approximately 2.76

[@rublade1]

Wolframalpha gives approx. 2.26 for the integral. The endresult Pi * ln(1 + sqrt(2)) is approx 2.76.

[@dodgsonlluis]

There is an error at 5:43 into the arctan argument, already noted in a commentary, that flaws completely the result.

[@inigovera-fajardousategui3246]

Shouldn't the derivative at 4:39 be the other way around [√(4-x)-√x]/[2√x(4-x)]? And also, there shouldn't be a 4 in the denominator at 5:01

[@krisbrandenberger544]

Correct on both

[@cyanide7833]

So when do i stop

[@ChuffingNorah]

Is there any physical model for this abstruse, arcane, arctan integral? It's a bit like String Theory being completely dissassociated from any testable real world physics? Maths done for the sake of doing Maths only!

[@bjornfeuerbacher5514]

I don't get the step at 4:50... how does he arrive at sqrt(8-t²) ?

[@minamagdy4126]

If you compute t²-8, you get (from the computed t²-4) 2sqrt(x(4-x)) - 4 = -x + 2sqrt(x(4-x)) - (4-x) = -(sqrt(x) - sqrt(4-x))² Simplifying this yields sqrt(8-t²) = sqrt(x) - sqrt(4-x) EDIT: corrected some typos

[@bjornfeuerbacher5514]

@@minamagdy4126 Thanks, I only got the first step and then wondered how to go on from there...

[@orionspur]

Noplace to stop!

[@ferenc_l]

Crazy integral from Azerbaijan

[@BikeArea]

When backflip? 👀✌️

[@roberttelarket4934]

The back flip done when he goes "back" from arctan to its inverse tan.

[@alquinn8576]

the way u draw square root signs gives me so much frustrage

[@johntse5770]

am i third?

[@Alan-zf2tt]

First 🌟

[@BikeArea]

Nope. 😊

[@Alan-zf2tt]

@@BikeArea you mus be in a later time zone no?

[@DavidWang-v7u]

Mike, you are one of the very few people that I know that still does maths channels on KZbin. Since you can make measurements based on the fact that Paleolithic and Neolithic Chinese People having Multiple Cradles as their Civilizational and Mathematical and Sciences Developmental Theories, the Mathematics based on Counting, like Whole Numbers and Real Numbers, most stuff that should diverge and should be sprung out of Humanities should be discussed, and whether or not those mathematics could be considered to have undergone any significant procedures or have been debunked, ranging from Vector Calculus, Number Theory, etc. etc. and also, those maths should also should not be deceived to be Whole Numbers or Integers so that they do not require critical thinking. The only problem is whether or not the other maths that do not coalign with these mathematics are able to lunge forward, destroy these maths as being mere Humanities Sciences, and able to contribute to the economies, or not..