@HayderAliBabul
the best explanation of e^-x2 integration............ everyone explains like the Simpson's episode.. rdr hardi har har.. thanks..........
@swimiborj5807
Beautiful, simple, clear, and elegant explanation, many thanks
@txikitofandango
Very nice demonstration that did not require Jacobian matrices and other transformations
@matiasaraya8083
I have to say the excellent job you did explaining this. I'm not a native English speaker, but I understood everything perfectly. Congrats
@MihaiNicaMath
I made a version of this explanation on my video on my channel for pi day this year! My version has some probability intuiton mixed in
@x.in_hype
Finally The Gaussian integral !! I already watched multiple videos on it but it was years ago I got a revision
@MathsAndPhysics
You can solve this using Hessian matrix to get extra R. From denoting x=Rcosa ,y =Rsina you can take derivative x by R which is cos(a) and by a which is -Rsina.Same operation for y and get sina , Rcosa .then create matrix I cosa -Rsina I I sina RcosaI If you calculate determinant you get R and your will look like double integral re^(r^2)drda where you can solve by interchange r^2 =t ,2rdr=dt
@Leo-di9fq
Great work!
@bhgtree
Thank you for this wonderful, clear and detailed explanation.
@ParaDox-xb3qw
My brain just exploded 🤯
@MostRightWingManInBritain
The correct answer is because it attracts lots of views and it boosts the algorithm performance
@creamcheese3596
Seriously though it's much easier to find the answer by differentiating under the integral as Feynmann liked to do. And he should know, he won a Nobel prize, though admittedly not for mathematics.
@Amelioration-ß
Gauss was pretty cool.
@OmarBenjumea
A masterpiece!
@KeepTechnic
You can do it with the gamma integral formula, and will be gamma(1/2) which is the square root of pi.
@amirmohammadvahedi4013
Of course enjoyed!
@Kier_but_who_cares
love this!
@farzadmf
Mind ... blown!
@gabygamerhd
cara muito foda, parabéns mesmo pelo conteúdo, muito simples e acessivel pra que tem o minimo entendimento de calculo e até pra quem nao tem, acho que fica claro de onde vem esse valor \pi, nessa prova eu nunca tinha entendido o motivo de I^2 ser igual a uma integral dupla, mas essa explicação de uma integral ser constante em relação a outra simplifica tudo.
@anushakamakshy