@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

@anushakamakshy

This is literally the first video you have ever posted in this channel that I actually was able to solve by myself. Thank you sir you always teach me something new And interesting

@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

@bhgtree

Thank you for this wonderful, clear and detailed explanation.

@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

@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

@qzorn4440

Most interesting information. 💯🥳✔️ Thank you.

@user-mathematicprof

Great, I really enjoyed this video, I have already subscribed to your channel, and I gave you a like for this great video.

@txikitofandango

Very nice demonstration that did not require Jacobian matrices and other transformations

@Leo-di9fq

Great work!

@mohammedpatel3051

Well explained

@ParaDox-xb3qw

My brain just exploded 🤯

@x.in_hype

Finally The Gaussian integral !! 
I already watched multiple videos on it but it was years ago 
I got a revision

@nikiniki586

Excellent😊🎉🎉🎉

@KeepTechnic

You can do it with the gamma integral formula, and will be gamma(1/2) which is the square root of pi.

@Amelioration-ß

Gauss was pretty cool.

@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.

@MostRightWingManInBritain

The correct answer is because it attracts lots of views and it boosts the algorithm performance

@21stCenturyNigeria

Cool video