DESTROYING THE DIRICHLET INTEGRAL (sin(x)/x) AND LETTING IT BURN IN THE 7th CIRCLE OF HELL

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Using Complex analysis: • A COMPLEX BOI! Integra...
Laplace f(t)/t: • Laplace transform: f(t)/t
Laplace sin(at): • Laplace transform: sin...
Let us burn this integral to ashes using laplace transforms! Enjoy =)
Twitter: / flammablemaths
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[@46pi26]

Today we witnessed the brutal murder of an integral. It had it coming.

[@Eta_Carinae__]

I never recognised how similar laplace transforms were to the feynman technique. Yeet.

[@RetsamX]

Maths and memes. M&M is always a good combo :)

[@darksecret6050]

M&M agrees

[@agrajyadav2951]

So is E&M

[@kevinb.3541]

He's finally gone insane.

[@user-sc2jz9ng6k]

kzbin.info/www/bejne/nojOZ32Zncp_g7c

[@markolazarevic4209]

Those intros are getting better and better :) Love them

[@duckymomo7935]

No, they keep getting worse and worse, you should send him hate Ps I actually love Flammable Maths

[@gregoriousmaths266]

jeez this was the eziest thing ive seen ever My God papa that integerahl had a family

[@Fightclub1995]

I like the arctan notation better than tan^-1

[@eliascaeiro5439]

Me too

[@Blackfir333]

Fightclub1995 yeah arctan is better, tan^-1 should equal to 1/tan :D

[@eliascaeiro5439]

XD

[@Fightclub1995]

Blackfir333 you know what I mean 😉

[@calyodelphi124]

I personally have a beef with the whole f^-1 notation because for some arbitrary unknown reason it's accepted that f^-1 is the "inverse" of the function whereas for all other values of n for f^n is simply the function f raised to the power of n... even though when k < 0 and |k| = n, f^k = f^(-1)(n). SO which is it at that point????? Is it the inverse function of f raised to the power of n for some power k < 0? Or is it just 1/f^n??? The logic completely fails at that point for the one special case where the power is -1. I'm honestly thinking about using I (that's a capital i because youtube is silly and uses a sans-serif font that has no bars on the capital i to distinguish it from lowercase L) in place of the power. So instead of writing f*-1, write f^I. It keeps the same "notation" of indicating the inverse function with something in the exponent, but explicitly uses the letter I for "inverse", thus freeing up -1 to unambiguously indicate the reciprocal of f instead of the inverse of f. What do you think?

[@Zzznmop]

I'm hangin out in the differential equation class tomorrow after calc from all your inspiring work with Laplace transforms, they just started lecture on the subject :~D

[@iamtrash288]

let it rest in piece. amen

[@PapaFlammy69]

r i p

[@manishivakr6513]

I searched this que. on Google n Google suggested me this one. ... You Entry was so COOL ❤Love From India😊😊😊

[@ChakraaAAAA]

😂😂😯wow the lord of destruction Mr flammable maths , unbelievable intro

[@saitaro]

Thanks for the video. I'm yet to learn this stuff though. What topics does complex analysis consist of?

[@apta9931]

Deine Videos sind ganz unterhaltend😁 Deine Erklärungen von deinen Lösungen finde ich auch sehr hilfreich danke

[@wduandy]

Amazing, for a long time i've wishing to see this integral be solved in that way.

[@gregorio8827]

That integral from -infinity to infinity is pi right? Since the function is even

[@skeletonrowdie1768]

niiice so this why the laplace transform can be so awesome

[@Sontraid]

I cant believe I just found this. You are amazing. Thank You :D

[@tomkerruish2982]

1:55 Justification by getting the right answer.

[@austinmitchell2652]

God I can't wait to learn this stuff next semester

[@MrRyanroberson1]

Derelict Dirichlet

[@tommasobruggi6614]

Very nice. Congrats

[@Absilicon]

I wish I knew wtf was going on.

[@Euquila]

Laplace transform re-casts the problem from one talking about "time" into one that talks about "frequency" instead. t (time) --> s (frequency). You solve the problem in this "frequency" domain, where the algebra is easy, and then you switch back at the end. You can even use the Laplace transform on differential equations.

[@gapdragon01]

Where is the 20 minute video where you solved this initially?

[@copperfield42]

so the first time it was like Goku vs Freezer, and this time is like future Trunks vs Freezer XD

[@thephysicistcuber175]

Dang, that is amazing

[@duckymomo7935]

You mean Flammable Maths is amazing

[@thephysicistcuber175]

Mi Les that too

[@zokalyx]

"I threw my chalk" lol

[@user-pn9zm8qg7k]

I'm just thinking can we burn a chalk

[@Mr4NiceOne]

Tan^-1

[@duckymomo7935]

ProbablyNotMe dat is not da wey!

[@poutineausyropderable7108]

It was 3:17 am when i started it. Now i'll go to sleep on a round number.

[@eliasarguello9961]

Can anyone explain why he was allowed to interchange the limit and the integral to get integral from t=0 to infinity of (lim s->0 (sin(t)/t * e^-(st))) dt?

[@eliasarguello9961]

In other words, how do you prove uniform convergence for that function in the interval (0,infinity) so that we can interchange the limit and the integral?

[@eliasarguello9961]

Never mind i learned how to do it using the dirichlet test

[@debendragurung3033]

thats fucking amazing, Im fucking subscribing

[@nootums]

Ex Deee Enjoyed the video!

[@nootums]

BTW, Everytime I watch your videos, I have to lower the volume in the intro part cuz my parents are around

[@nathangazo2043]

I wanted to activate the subtitles but youtube has decided that your video was in german lol

[@quantumchill5237]

Dirichlet integral 🅱estroyed

[@mipmip4575]

btw, is your discord server full or can people still join?

[@copperfield42]

where is your long video on this? I wanted to check it out too

[@copperfield42]

thank. no wonder I could no find it, you start from a different place

[@SiySoloSiMath]

*Nice vídeo!*

[@eliascaeiro5439]

Amazing!!!

[@holyshit922]

I saw this solution on the video recorded by Spanish guy

[@fidgetspinner1050]

OMG REKT U M8 DIS INTEGRAL HAS BEN *********!!1!1!!1!! RIP

[@aman_xo]

My math teacher said this integral is not solvable.

[@IFone456]

and what if it has no limits defined? I'm pretty sure that's the one the OP means

[@zokalyx]

just like gaussian

[@juijani4445]

ezee r i p chhak

[@azmath2059]

How did you go from (sint/t)e^-st to L {sint}φ ?

[@azmath2059]

Flammable Maths: Ah! Very clever Laplace re-arrangement indeed.

[@gagi3470]

@@azmath2059 Please could you explain this rearangment. It is maybe some subtitution?

[@gagi3470]

@@azmath2059 Ok, I found !!😊

[@khatharrmalkavian3306]

What?

[@thalostv8991]

Might i ask you, would you help me by maybe posting my youtube channel link in your description, i will start this week by posting math videos regarding analysis and such , cool integaras and so on , i would be very thankful . Ofcourse not on this account , but another one i created for such purpose, i just want to know if you would help me out a bit like that

[@PapaFlammy69]

nah

[@ianmathwiz7]

*reads title* Well, that escalated quickly. Seems a bit of an overreaction to a maths problem but w/e.

[@suneetiyer81]

what exactly are laplace transforms? I know nothing about them :'(

[@46pi26]

Flammable Maths actually has done some really great videos on them; basically, they're like the big sigma notation you'll see for a power series, but coverted from a discrete variable n to a continuous variable t. There's some video from MIT if I'm not mistaken explaining the meaning behind it.

[@suneetiyer81]

46 and pi ok. could u Send the link. I'll watch it.

[@46pi26]

Melody Agario Flammable Maths' explanation: m.kzbin.info/www/bejne/eWLGk5R6fsaJoK8 Here's the idea behind the Laplace Transform: Part 1: m.kzbin.info/www/bejne/sKfFlaKJmqx0nas Part 2: m.kzbin.info/www/bejne/nqKyk6KMZ8-ajNE Hope these help!

[@suneetiyer81]

46 and pi Thanks a Lot! !!!

[@46pi26]

Melody Agario You're welcome! I love seeing people learn!

[@Blackfir333]

Nice moonwalk lol

[@deyvismejia7529]

Does math rule the universe or does it describe it?

[@smitashripad9757]

Starting was really bad

[@blackpenredpen]

THAT INTRO WAS LIT!

[@whozz]

Great video. I understood nothing at all

[@whozz]

@@PapaFlammy69 But now I do. A semester of Calculus 2 did the thing. Thank you!

[@megauser8512]

lol

[@jeanveramorocho9307]

@@whozz Tell me about character evolution

[@igorface09]

@@whozz You learned the Laplace transform in calc 2?

[@mrhatman675]

@@igorface09 me

[@faith3174]

Gottem

[@swift3564]

1:16 Is that a really small euleroid at the bottom right?

[@PapaFlammy69]

yeye :p

[@duckymomo7935]

Worst intro ever, ie i can’t believe you moonwalked, love ya

[@ThAlEdison]

Maybe a song with pop-punk progression arpeggiated everything chords might sound nice.

[@PapaFlammy69]

:D

[@ThAlEdison]

@@PapaFlammy69 So this comment was actually meant for another video, and I don't now how it got hear. But fate has let me give the Papa a smile.

[@FutureAIDev2015]

Can you make a video where you attempt to integrate the system: dv/dt = (9.81 * (4077440 / (4077440 + h(t))^2) * (n - sin(b(t))) db/dt = -((9.81 * (4077440 / (4077440 + h(t))^2)/v(t)) - (v(t)/(4077440 + h(t)))) * cos(b) dh/dt = v*sin(b)

[@calyodelphi124]

I never thought I'd see a math video with such a clickbaitey title, but here it is. And you totally delivered what the title promised. Fuckin' ace. :thumbsup:

[@Czeckie]

cool as fuck. Please, teach us other integral transform

[@alexander51413]

I know nothing about Laplace transforms, however when watching I saw that this was fairly similar to blackpenredpen's video titled "The main dish, integral of sin(x)/x from 0 to inf, via Feynman's Technique" (which I understand fully). I know a quick google search will probably fix this, but while i'm here, what is the relationship or is it just a coincedence?

[@alexander51413]

that fact that both of you multiplied by e^-bx, though with your video it just popped up when you mentioned "laplace transform" and also that 1/((whatever)^2 +1) also apeared in both videos. tbh I should probably research what laplace transforms are before this, so there not really any need to explain, but thanks for the great video anyways!

[@oscardavidalarcon2673]

Buen video. Flammabler maths

[@sarpkaplan4449]

hey flammy, how many people you want in your discord

[@sarpkaplan4449]

ı would love to

[@agrajyadav2951]

Kya kar ke solve kar diyaa yaar!?

[@jihanhamdan5465]

That's awesome man i loved the title also

[@dackid2831]

Papa Flammy, I have a question. Why was the Laplace transform on the integral equivalent to the value of the original integral? Shouldn't they be different values? If not, then why is that? I just need this one thing cleared up: that would be greatly appreciated.

[@PapaFlammy69]

We took the inverse at the end making it equivalent again :)

[@okhan5087]

667th like

[@stydras3380]

YAY C:

[@lok7396]

Where do you learn about Laplace transforms and what basis do you need to have? I know a bit of complex analysis but maybe I'm not advanced enough.

[@yuval2be]

Not about this video, but how do I do that: sin(1/x)*sin(x) and x->0 (x goes to zero). Thanks

[@mipmip4575]

You are terminated

[@measurezero]

Hey am I allowed to join the discord?

[@piotrliach]

that was ruthless

[@MaxwellsWitch]

WHAT A MADMAN!

[@lpu_n.4926]

What a title x)

[@sansamman4619]

Is it bad that I don't know what's " the 7th circle of hell " ?

[@sansamman4619]

Flammable Maths, phewwh I thought it was a math thing like the name of the 7th unit circle or some stuff like that