Destroying the Gaussian Integral using Papa Leibniz and Feynman

[@moc5541]

In approximately 1971 I attended a seminar by Feynman on the PCT theorem at UC Berkeley. The auditorium had sliding black boards as in this video except that they were huge and heavy and so they hung from pulleys with one of the boards serving as the counterweight for the other. Feynman, upon sending up one of the boards to write on the other said to the audience "Oh look. I don't have to do any work." Laughter from the all-physicist audience.

[@gnikola2013]

14:29 This is outrageous

[@MaksiZockt]

10:41 the best thing to do as a german... xDDD

[@prydin]

DON'T MENTION THE WAR!!!! :)

[@nathandupont8939]

Godwin point my bois

[@duckymomo7935]

Maks not C!

[@yodaadoy2863]

As a german, and behalf of all Germans We will remember this flamy, and so will the wall street journal

[@jtbauer3789]

Gaussian represents some sort of symmetry which in 3-d can be built up by infinitely many slices of "disks". With that, it, no wonder, is somehow related to Pi.

[@NoNTr1v1aL]

10:04 mah boi's board has been possessed by Papa's soul.

[@NoNTr1v1aL]

14:14 OMG that celebrity's name is Sharukh Khan and my mother was his fan and that's why she named me Sharukh. Coincidence? I think not.

[@galek75]

*Sips* Reminds me of the time when Kant tried to destroy traditional metaphysics

[@emmanueloluga9770]

Hahahha yeah, that was indeed funny. More so. I don't think its so much of Kqnt trying to destroy traditional metaphysics than it is him being irresponsible epistemology

[@stydras3380]

2:59 the CHEN LUUU!

[@CallMetheMusicMan]

I just discovered this channel and I freaking LOVE IT. Flammable Maths is awesome!!!

[@CallMetheMusicMan]

Flammable Maths enjoying is an understatement! :D

[@yannld9524]

Ok but it works only if a>0 !!

[@AlexMinos]

Or Re(a)>0

[@Davidamp]

@@aidankwek8340 Integral wont converge in all cases

[@Fematika]

14:13 Great picture of Dr. Peyam.

[@all462]

Is he Shahrukh Khan from India?

[@KamleshSharma-gc8jv]

@@all462 yuuup

[@vicenteagost1895]

Hi there, dude. Love your vids. At minute 14, what if the parameter "a" is negative? Wouldn't it lead to a non convergent integral? Brilliant! Keep going.

[@PapaFlammy69]

yes, a>0 is required!=)

[@mudkip_btw]

I like how in these older videos you make a few more mistakes, still the content is great do like it very much! Papa bless

[@PapaFlammy69]

:)

[@masteryoda1748]

Alright,I wont be going to school now...Watching ur videos is enough

[@dannygjk]

lol

[@divyyy4358]

You are a genius. Period. Just shared this video with 5 others

[@ozzyfromspace]

Greetings from America and Africa! Have a Flammable day, bro! 😊🙌🏽🎊

[@amogh5427]

Thank you... It is helpful in solving quantum mechanics problems

[@jenpsakiscousin4589]

Mathematics sounds so much better on chalk than a marker board

[@hinmatth]

13:37 This limit, we'll dominate :)

[@oni8337]

1337

[@gammaknife167]

Nothing less than a cool video! Haven't learnt some of these integration techniques yet, so I know how I'm gonna spend this evening!

[@abdullahm4830]

At 7:48 Don't forget the negative sign my boys! Jens : 'My girls' are smart. Only boys need a reminder! 😂

[@PapaFlammy69]

:D

[@andreapastore4287]

That's some nasty integral

[@bingusiswatching6335]

i like how it sounds like a youtube apology video in the beginning

[@harry147ish]

PHYSICS STUDENTS: change to polar coordinate plane --> done

[@PseudoMystic]

Subbed and favorited immediately upon seeing "Papa Leibniz". Haven't even watched the video yet and I still can't do calculus.

[@sach7762]

Had to come over here and hand out a like, just because of the title.

[@PapaFlammy69]

:D

[@illumexhisoka6181]

I allays wondered what π have to do with this integral The moment i saw Invers tan i felt it Thank you very much 🥰 finally a solution that i can understand I am a high school student by the way

[@markolazarevic4209]

Thanks for this video man! Keep going u are the best

[@AndDiracisHisProphet]

Nice picture of Dr Peyam

[@blackpenredpen]

AndDiracisHisProphet where?

[@blackpenredpen]

AndDiracisHisProphet nvm got it at 14:14

[@arjjanwalia5939]

@@blackpenredpen That's actually the Indian actor Shah Rukh Khan

[@gustavosedano294]

Oh my god!!! Gauss could be angry :v. Just amazing!

[@SultanLaxeby]

Don't you have to use uniform convergence in order to interchange integral and limit at 13:25? Because that's not allowed in general. For example, observe the integral from 0 to 1 of n*x^(n-1) dx and let n go to infinity.

[@ShubhamKumar-on8kz]

I am from india....this concept come so many times in gate exam ...tq brother...🙏🙏

[@gregoryfenn1462]

At 2:00, how did we know to square the I(t) integral? Like, trying to solve it, what clues are there that this is a useful step?

[@user-pn9zm8qg7k]

I found the general method, it is more geometric it change I(x) to (I(x))^2=I(x)I(x*)=I(x)I(y)=V(x,y) so we need to integrate z(x,y)=e^((-a)(x^2+y^2)), plot on 3 dimension the integral basically is finding the volume between z(x,y)=e^((-a)(x^2+y^2)) and z(x,y)=0 we found symmetry around z axis, so we change the coordinate to cylindrical coordinate the original integral=z(x,y)dxdy=e^((-a)(x^2+y^2))*dx*dy intergral after=z(R,angle)dRd(curve)=e^((-a)R^2)*dR*(Rd(angle)) the additional R from d(curve) made the integration solvable them I(x)=(I(x)I(y))^0.5, solved I still like your method more Your method is much easier to understand

[@kameronshope6637]

This could also be solved for by using the gamma function (a lot easier imo)

[@pallavjain6216]

If a

[@user-wu8yq1rb9t]

*Papa* ... I miss you and your Math .... Therefore I'm here, because your old videos are still great. Thank you *Papa Flammy Mathy* . *Papa's Ways, Is The Best* . Your Hagoromo Chalk and Your black jacket 😂

[@amithawanigasooriya5645]

Extremely a mad genius

[@Soundillusions94xyz]

I LOVE YOU Watching you do this is very satisfying. Where did you learn these techniques? In graduate courses? I'm an engineering student but these techniques are never mentioned in my calculus classes.

[@srpenguinbr]

I have learned how to solve exponential equations lately. I faced a problem that required a substitution t=2^x and t ended up being negative. Well, no problem, complex numbers helped me and I got the result. My teacher had never heard about such a thing. Note she has a masters degree. Thank you, mathematicians of KZbin.

[@SirDerpingston]

where do you find such thorny integrals? I'm looking for some hardcore calculus questions...

[@michaelboyd8546]

@@SirDerpingston e^[-(x)^2] is a famous function because 1.) It is the general shape of bell curves used in statistics and 2.) It's integral is non-elementary, which I find pretty interesting

[@josephgrossenbacher7642]

@@PapaFlammy69 , that's the only way to really LEARN , DO & UNDERSTAND maths ... !!! ... & you also 'did well' , so thanks !

[@polychromaa]

@@SirDerpingston michael penn on yt and this channel have some meaty integrals

[@jmate2321]

Making a bit complicated but I love your approach ...

[@sofianeafra6161]

You look angry in the video debut 😂😂 I like you 🔥

[@sheeniebeanie2597]

i got asked to solve this for an interview and i am going to use this next time i get asked to BLOW SOMEONE'S MIND.

[@magnuswootton6181]

You know what would actually be good, is if you can use guassian blurs to do filters instead of IIR/FIR if you can just increase the fall off!!!

[@FernandoVinny]

Are you interested only in real/complex analysis? What about Abstract Algebra, Combinatorics, Topology, Number Theory etc...?

[@MrAssassins117]

It must be so fascinating, any dislike in your videos i guess, thats a proof that your channel its a lot useful, fellow :)

[@Czeckie]

lol, you approach the problem of interchanging various limiting processes as every professional analyst I know: "just fuck it"

[@Czeckie]

but the video and technique are lit af

[@FernandoVinny]

Man you're so cool and handsome

[@dr._rayan2807]

why does he feel like crying but resisting it the best he can

[@ryanjagpal9457]

Partial derivative, t and +c: Hey Me: Have mercy please Them: There is no mercy Also the only thing in this that makes sense is dt/dt=1, the rest just makes no sense, sik why calculus was even a thing, like it makes no sense

[@Legacies87]

Wow really awesome

[@user-ic4kq7uu6x]

Is it possible to evaluate integral e^-(x^3) 0 to infinity the same way?

[@AmusWhite]

7:30 The u=x/t therefore it is dependent on t, how could you ignore the chain rule in the partial differentiation step?

[@digxx]

nice approach.

[@andrewsantopietro3526]

Hey I just wanted to ask about when you are solving for the c value, you don't touch the variable u even though it is dependent on t. As I recall, t is equal to zero, and u is equal to x/t, which would make u undefined. I would just like to ask how it still works even though that part is unresolved. Thank you so much for your effort and I'm loving your videos!! There really is a uniqueness to your videos that I don't think I've ever seen except kind of in Faculty of Khan, who is just pure salt and no more. This really blew my mind on several levels, so I'll use papa flammy's method every day in my calculus class, referring to it with that name every time because there is no other more beautiful way to describe it.... I don't know how but I'm going to try anyway XD.

[@dmitrii.zyrianov]

Nice video! Why did you use the same letter (I) for constant and for function?

[@waldersasytz4274]

you could do it in one action by dividing and multiplying by the root of A and substituting A under the differential

[@fredi1505]

Me after watching the first episode of Rick and Morty

[@dannygjk]

"is nothing else but", is nothing else but, "is just". ie. "is nothing else but" simplifies to "is just". XD Sorry I couldn't resist a silly joke. :P

[@SiddiqueSukdiki]

i love you papa flammable maths;

[@sansamman4619]

I know that pi is half a circumference. was he talking about circles?

[@duckymomo7935]

San Samman a circle is 2pi radians, radians is standardized in the unit circle so it’s just 2pi

[@rockybond42]

I've gotta know, what song do you use whenever you introduce the problem?

[@IlTrojo]

NICE! I only missed what if a

[@dlevi67]

1:32 We call that bad boy "you""? OK, if you insist. Thanks for the video!

[@youplaylist6810]

At 12:00, if we make t = 0, doesn't that mean u = x/0 which isn't allowed?

[@repressible_operon]

Hello. I'd like to ask why u was considered a constant at 7:15 when u was defined as x/t. Thank you.

[@jacobbills5002]

Just watch this impressive Math channel kzbin.info/door/ZDkxpcvd-T1uR65Feuj5Yg

[@a.fleischbender7681]

Shouldn't the domain of a be a>=0? If a∞) doesn't converge, right?

[@PapaFlammy69]

yas!

[@a.fleischbender7681]

@@PapaFlammy69 Thanks for quick answer, Papa Jens

[@PapaFlammy69]

[@tomatrix7525]

Lovely stuff

[@ΔημητρηςΠαπαγεωργιου-γ2υ]

a belongs to R.Doesn't that mean that when a is negative the integral is not finite?

[@Armytechrex]

if Gauss revives and sees this bad boi he will get mad indeed :v

[@prakharmathur9453]

Brilliance incarnate.

[@EmissaryOfSmeagol]

Papa Bless

[@JanPBtest]

3:08 There is just one term there equal to exp(-at^2) by the usual fund. thm. of calculus.

[@late7245]

Can you calculate fx= (1/2)*sqrt(1-x^2); Integral(f'/sqrt(1+(f')^2))dx Use any method to achieve this? Eliptic curve length?

[@suhailbhat1996]

Area property of Fourier transform doesn't give correct answer for this integral. Why? I mean this property, area under the curve of f(t) = F(0).

[@bouteilledargile]

Good morning to you too my flammer

[@shersinghsaini8510]

Papa's way is the best

[@chispun2]

What can be done about the quotient of two of them? Like one integrated until 3 and other until 5, or so?

[@eliascaeiro5439]

Why tan^{-1}(x)? Why? arctan(x) is so much better ! tan^{-1}x=1/tan(x)=cotan(x) ! Other than that, great video.

[@AndDiracisHisProphet]

context, my friend

[@AndDiracisHisProphet]

also i think it is important to remember that "to the minus 1" doesn't mean "1 over" but "inverse". It just happens that the inverse of simple numbers is also denoted as "1 over"

[@sansamman4619]

inverses are just weird in trigonometry. go look up: pre algebra. I'm kidding 😂

[@rexwhitehead8346]

Lord Kelvin's definition of a mathematician: Someone to whom Int[-infty, +infty] exp(-x^2) dx = sqrt(PI) is as obvious as 2+2=4. (Said before Russell and Whitehead rendered 2+2=4 non-obvious to anyone.)

[@leonardofigueiredosaraiva9849]

Can you solve the integral of x².e^2x² dx from -infinite to +infinite?

[@정구-x2e]

14:16 Did you consider the case which a

[@احمدفليح-ق7غ]

great .thank you .... is x variable real or complex ?

[@isakhammer6558]

great video!

[@timothyaugustine7093]

Where did you get the chime music at the beginning (when you show the question)?

[@azizlokhandwala2345]

Hey, I want to know whether this integral could be solved or not(integral from 1 to inf(lnx / (x^x)))

[@rapidfire9130]

why is the comments section blocked for the new videos, does any one know???

[@natepolidoro4565]

4:10 MY EYEBALLS!!!

[@paulraj7573]

genius papa

[@dev02ify]

But you still used the squaring trick. How about doing it purely with a parameter and differentiation under the integral?

[@ozzyfromspace]

*Link in the description to the corresponding video* 😂😂😂 Yes bro

[@ShivamChauhan-xe7zi]

Legends only know that he was earlier known to be "Fapable maths"😂😂😂

[@ゾカリクゾ]

This was super cool. However I have a problem: You introduced u as x/t and then you treated u as a separate variable, for example, when you took the limit as t goes to infinity. Are we allowed to do that? I mean you got to the correct answer, so I suppose there must be some validity in what you have done...

[@michaelmischko847]

Dont say that - you easily get correct results from doing wrong maths, so your question is legit. My guess looking at it would be that you got lim t²(u²+1) = lim t² = inf (because lim u²t² = constant) and lim u²+1 = 1 and thats why he doesnt even mention that u = u(t).

[@YourMakingMeNervous]

I have a question. at 12:00, if we make t = 0, doesn't that mean u = x/0 which isn't allowed?

[@youplaylist6810]

Did you ever solve this question? I am having the same problem understanding. @flammablemaths @YourMakingMeNervous

[@moehassan_]

4 years late but that integral was in terms of x, so we're plugging 0 into x, and t into t.

[@noutkleef4458]

What's the name of the . : (three dots) symbol used as "therefore"?

[@eeeeee68ci]

Ik this is not related to this particular video but still, how do you know what contour to draw when you're doing complex analysis? Can't find the answer please help!

[@eeeeee68ci]

@@PapaFlammy69 should I use some sort of a graphing tool?

[@eeeeee68ci]

@@PapaFlammy69 Also thanks for making these videos, they helped me understand Calculus a bit better :D

[@ChrisChoi123]

fellow mathematicians fllow mathemacians flow mathemains flo mathmans flo mamans flo amas fl amas flamas = flammers

[@Saptarshi.Sarkar]

I will still use the Gamma function though

[@janderson2709]

Brilliant. But which element that you used was Feynmann?

[@janderson2709]

Flammable Maths That makes me pleased since I have one more thing to learn rather than two. I'm in second year maths at the moment of a 3 year BSc. Is this technique something that's typically covered in degree courses?

[@Rafi-be2ij]

great video! where would you say is the best university in germany for mathematics? (im currently learning german so hopefully the language of study wont be a problem)

[@ttttt_]

From what I've heard TU Munich is the best.

[@RijiVids]

hello pappa flammy I was wondering if you know the book Inside Interesting Integrals (You might like it)

[@RijiVids]

You should, I think you can get some good inspiration out of it for your videos In fact, iirc the exact integral you did appeared in that book and was solved using the same method lol (which is why I was reminded of the book) I have a... 'totally legal' pdf of it if you're interested

[@ThePacificOc]

LEOriginal037 Where can I find the "Totally legal" pdf for this book?

[@AndDiracisHisProphet]

That's just the "Theoretisches Minimum" for physicists^^

[@andromedarobinson777]

Lookin rough, my guy. You doin ok?