Gaussian Integral [Int{e^-x^2} from -inf to inf]

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In this video, I showed how to integrate e^-x^2 from -infinity to infinity and get sqrt pi as answer

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Would be interesting to recollect how Jacobian is introduced, and how it's inferred in general

lukaskamin

Great explanation. One wouldn’t even need to know multivariable calculus to understand this.

znhait

Very smart. The result sqrt(pi) is related to circle or polar coordinates. Coordinates conversion simplifies the solution.

briandong

Very elegant solutions. Congratulations!!!

Josedepalmares

best explanation video so far however i think it would have been better to show change of variables more in depth using jacobian

chaosforever

Great explanation and blackboard technique!

tcmxiyw

For the first person tanks for an other video ..teacher

masoudhabibi

I remember when I thought this technique smacked of trickery. Then I learned of Feynmann's technique and the world stopped making sense altogether.

kingbeauregard

I know this sounds like a silly question but how did you get to understand such situations in math? Was simply reading the textbook helpful/did you need to read or procure other resources? How did you find them and know the difference between what would be helpful vs what would not? Thanks a lot, fascinating video as always.

HMS_GMS

You are so so great guy!! Thank you :))

kemalbarishatipoglu

when you said the jacobian could be shown in a different video, I got sad cause that's what I wanted to see lol
otherwise, this was cool to watch :)
I've used the gaussian integral a bit recently in my physics classes, but never really knew where it came from.
Also, sqrt(pi)/2 is (1/2)! I assume they're related.

WingedShell

Is the derivative of pi equal e<-xsq>?

AliBaba-ztw

Recently is solved by Double integral and transfer it to polar ordinance and no need use IxI ?

nickzadeh

One thing that is passed without saying explicitly is that Z is an integer in this derivation. This is therefore not a general definition

marcinandrzejak

What does e have to do with e^-infinity like any value to ^-infinity is 0

blueschase

Does that mean I have to watch like 2 other videos just to understand the full concept?

akeredoluoluwasogo

I saw a sped up proof of this and it was going into matrices and all sorts, has anyone come across that before?

joelmacinnes

Gaussian Integral [Int{e^-x^2} from -inf to inf]

Gaussian Integral [Int{e^-x^2} from -inf to inf]

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