the best explanation of e^-x2 integration............ everyone explains like the Simpson's episode.. rdr hardi har har.. thanks..........
Beautiful, simple, clear, and elegant explanation, many thanks
Very nice demonstration that did not require Jacobian matrices and other transformations
I have to say the excellent job you did explaining this. I'm not a native English speaker, but I understood everything perfectly. Congrats
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
Finally The Gaussian integral !! I already watched multiple videos on it but it was years ago I got a revision
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
Great work!
Thank you for this wonderful, clear and detailed explanation.
My brain just exploded 🤯
The correct answer is because it attracts lots of views and it boosts the algorithm performance
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.
Gauss was pretty cool.
A masterpiece!
You can do it with the gamma integral formula, and will be gamma(1/2) which is the square root of pi.
Of course enjoyed!
love this!
Mind ... blown!
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