@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

@swimiborj5807

Beautiful, simple, clear, and elegant explanation, many thanks

@bhgtree

Thank you for this wonderful, clear and detailed explanation.

@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

@HayderAliBabul

the best explanation of e^-x2 integration............ everyone explains like the Simpson's episode.. rdr hardi har har.. thanks..........

@x.in_hype

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

@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

@KeepTechnic

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

@Leo-di9fq

Great work!

@Amelioration-ß

Gauss was pretty cool.

@ParaDox-xb3qw

My brain just exploded 🤯

@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.

@MostRightWingManInBritain

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

@OmarBenjumea

A masterpiece!

@Koro7667

What type of software are you using to display 3d graphs?

@R_man740

Nice one. But  can you tought us the Jacobian method so that we can be able to solve any type of this integral. Which polar substitution

@21stCenturyNigeria

Cool video

@chitradevi9919

Bro u should do electricity all the Kirchhoff laws pls