well the most intuitive way to make it possible to integrate is to keep the quadratic terms in the exponent while adding a multiple of y (or x), so that's where the substitution x = t*y comes out
Whenever you see something it is curvature. Image a straight line and give a twist in whatever direction. Twisted such things give time relationship to straight.
I dont understand why e^y^2(t^2-1) has an anti derivative by not e^x^2? Surely if you take t =0 you would get the same form as e^x^2 but just with y instead of the x variable
@@drpeyam well e^x is a function, but e itself isn't... But it's so common for e to be at the base of a power that it can be thought as a function, I guess
I've been waiting for a non multivariable approach to the gaussian integral all my life! Thank you SenPI
"Oh, I want to know more about Gaussian integral ... and can you please change my diaper".
@@PackSciences sorry dude but I had to
ua-cam.com/video/OLpeX4RRo28/v-deo.html
@@PackSciences Get outta here with your elitism
@@yaaryany perfect reply . lol
@@darkseid856 haha yes :P
This is arguably the nicest way of doing it.
Flammable Maths where you at? 😂 We need a similar interesting integral boi done in 12 ways :3
Wow! I didn't thought that it will be so impressive. Well done!
I'm hoping to be blown away by some radically different method which does NOT involve Papa Foubini. But this is nice too.
Oh, you’ll be mind-blown for sure, just wait 😉
Keep going Dr. Peyam.
You are my favourite youtuber.
it´s hard to forget with u; thanks my friend!
Polar coordinates are way easier.
However this method is also interesting. ☺
Fresh try never seen before. Good Job. :-) Thumbs up
I love your enthusiasm!
'Let's do the Spiel'😂😂
You are awesome Dr Payam. Keep it up.🌷
Looking forward to the complex integration variant.
That’s Way 11
I love this method!
Please teach us about more ways Sensei!
10 more ways to come!!!
Perfect substitution 👍
What I can’t get over is how do you know that the multi variable integral is still the same as the single-variable integral?
What am I missing in generating the differential? The differential of x = ty should be dx = t*dy + y*dt?
Thanks for the sharing! Just wondering how to come up with the t-substitution with t=x/y but not other stuff? Thanks
well the most intuitive way to make it possible to integrate is to keep the quadratic terms in the exponent while adding a multiple of y (or x), so that's where the substitution x = t*y comes out
I got a question Dr Peyam, any of the 12 ways you'll show us of calculating the Gaussian Integral involves using the power series of e^x?
Actually no, because you’d have to plug in infinity in your power series, which is weird
you said t^2+1 is constant for y.....
but why didnt you multiply it on the upper sidr...
cause this wasnt written before..
Love this method 😍
Whenever you see something it is curvature. Image a straight line and give a twist in whatever direction. Twisted such things give time relationship to straight.
Dr. Peyam what's about fubini theorem?
I dont understand why e^y^2(t^2-1) has an anti derivative by not e^x^2? Surely if you take t =0 you would get the same form as e^x^2 but just with y instead of the x variable
That’s the beautiful thing, complicated functions can have antiderivatives while simple ones sometimes cannot
@@drpeyam if you diffeientate y^2(t^2-1) wrt y then you get 2y(t^2-1) not 2(t^2-1) in the denominator?
My bad i didnt see the extra y term which cancels it out at the denominator
Incredible. Thank you very much.
Gracias amigo
This was amazing!
Perfect way!
Very very great video
Gracias. Muy interesante, muchas gracias.
Sir , please sell your t - shirt 👕 ....😘😘👍..how to made it ?
This looks really cool but I'm doing a level right now so I don't get why it's equal to e^-y^2 dy
@sonnenwind thank you! I was imagining a x=e^y^2 plot on a Cartesian graph but I realised that it's 0-∞ on the y not the x axis!
Just amazing!
Papa Peyam's Advent Calendar XD
O-i-a-a
In an old calculus book I have
It's called Poisson's integral and not "Gaussian" why is that?
Buy a different book.
Can a elliptical integral be evaluated?
No
Where’s the shirt from??
You can get it from blackpenredpen’s Teespring shop
Why is J²=(.....) ydydt?
Where did that "y" come up?
See 2:31. It's a consequence of u-substitution.
@@sethgrasse9082 thanks, I see it now
brilliant!!
I like this one in the video.
So cool! 😍
Best Friend!!!!!
GAUSSIEN INTEGRATION EN FRENCH EST CE POSSIBLE MERCI DE VOTRE COMPRÉHENSION
Oui pourquoi pas? Haha
@@drpeyam BEN ALLONS Y DOCTEUR PEYAM 😜😁👍👍
The Gaussian Integral is my favorite integral
Still uses fubini, so still a multi variable approach.
Please next method do by feynman law....please sir
That’s method 4
@@drpeyam okkk..then i'm waiting...
*Feynman's trick
@@HilbertXVI yup...
Fun little u sub
Just understand the "usual way" then this thing ruin everything that I understand
Why do you say "e OF something" and not "e TO THE something"???
You make it sound like it's a function and not a simple constant
It’s shorter to say!
And it is a function! f(x) = e^x
@@drpeyam well e^x is a function, but e itself isn't... But it's so common for e to be at the base of a power that it can be thought as a function, I guess
Some people use exp(x) instead of e^x. Looks more function-y that way
This is " historical solution" for this question.You should explained without saw note.
?
You really need to adjust the camera angle, it's really hard to see far end of the white board
#oreo
wowwwwwwwwww
Ouu have weird accent. Kinda like Prof. Walter Lewin or some old man.
communist russian disagrees
we-substitution is better