The Single Most Overpowered Integration Technique in Existence.

[@NightwindArcher]

As a physicist myself I appreciate your talent for wild rounding. Thats something I can get behind.

[@PapaFlammy69]

:D

[@TheLucidDreamer12]

Engineers too

[@paolosalerno6633]

@@TheLucidDreamer12 you forgot to approximate your comment

[@insouciantFox]

Astrophysicist: order of magnitudes only.

[@mustafizrahman2822]

Can you suggest to me how to be good at Physics? I want to be a Physicist in the future. Please suggest me.

[@angelmendez-rivera351]

*The answer is around 6 or 7... let us just approximate it to 1* I died

[@silentobserver3433]

Especially considering the answer is actually around 30

[@PapaFlammy69]

~1 great meme, ngl

[@hoodedR]

Lmao same

[@MrLikon7]

as an engineer, your weakness disgusts me

[@PedroKrick]

If it's around you can round

[@riakm921]

0:15 Phlegmmable Maths

[@PapaFlammy69]

*r i p*

[@someoneuppingdudetechnical6320]

F

[@2false637]

I’m 100% going to troll my teacher with this one but then get a zero because he didn’t understand it

[@PapaFlammy69]

rip

[@duncanw9901]

Haha wolfram alpha can't find a closed form of the final integral ladies and gentlemen: we gottem

[@PapaFlammy69]

:DDD

[@NightwindArcher]

Thats not actually true. I typed it in and wolfram got the right answer

[@duncanw9901]

@@NightwindArcher yea 'cause it numerically integrated i.e. cheated

[@hive9375]

Ladies and gentlemen *We gott'em*

[@lucamuscarella4085]

@@duncanw9901 Seems like this is implemented in Wolfram Mathematica. It finds (exactly) correct answers to integrals of this form

[@rishavmukherjee4251]

9:18 "And now we're going to create ourselves an absolute abomination of an integral and we are just going to rip its ass wide open" I DIED MATE

[@PapaFlammy69]

:D

[@integralboi2900]

My first instinct when I see an integral like this is to check if the function is odd.

[@PapaFlammy69]

same :)

[@Speed001]

My first instinct is to never encounter it.

[@nikhilnagaria2672]

If not, just 👑

[@bruh____784]

My first instinct is to inhale chlorine gas

[@frozenmoon998]

Me before watching the video: *1 + 1 = 2* Me after watching the video: *so we can integrate everything there is, as long as we have Papa's brilliant method*

[@PapaFlammy69]

:D

[@lucabayne2874]

Congratulations on getting references on Wikipedia bro, really looking forward to your proof of e=1

[@timurtheterrible4062]

Last time I was this early the Pythagoreans were killing Hippasus.

[@PapaFlammy69]

ezzzzzz xD

[@LB-ky9hg]

Isn't t(x) restrained to being an even function (not any function), because, if it's not, t(x)^o(x) * t(-x)^(- o(x)) = 1 is not valid?

[@PapaFlammy69]

Oh, probably! Thanks for the constructive comment!

[@angelmendez-rivera351]

Yes, it is necessary that t(x) = t(-x) in order for the result derived to be true.

[@duncanw9901]

t doesn't have to be continuous though as long as that property holds 😈

[@bfnnyelf]

@@PapaFlammy69 i think t should be restricted to be non-negative on the interval, so you can apply that t^o × t^(-o) = 1 for all x :)

[@kukuster]

the example indeed does work out though

[@steve112285]

For the annotation at 9:25, I think you mean t can be any even function of x. If t isn't even, you don't get the same simplification to 1 when combining fractions.

[@PapaFlammy69]

Yup, already noticed!! Thanks for the comment though Steve!

[@ARBB1]

I can't believe the official Wikipedia article on the lists of integrals links to this video lmao

[@alwaysbored47]

So wait...it happened 2 months ago? Whoa!

[@sofielundsskolan]

"official" Wikipedia article. Do you even know how the site works?

[@donaastor]

so tragic someone removed it. fucking vergins

[@ziquaftynny9285]

@@sofielundsskolan You clearly don't. :)

[@geek12098]

So now we have math formulas to come up with clickbaity thumbnails ? Now that's meta.

[@PR_7]

The first time I saw f(x) written as a sum of an even and odd function was in Paul Nahin's book "Inside Interesting Integrals," and this was just as spectacular as when I first read it. The idea is so clear in hindsight, that it begs the question: Who thinks of this stuff? Wish it was me lol. Great stuff.

[@PapaFlammy69]

:)

[@거미남자_spidy]

Great integral!

[@PapaFlammy69]

thx Zerg :3

[@거미남자_spidy]

kzbin.info/www/bejne/aqXPf4acgppmnpI

[@3manthing]

Your enthusiasm and sheer happines(like at 10:33), makes watching your videos me enthusiastic and happy.

[@PapaFlammy69]

Glad you liked the video Benjamin! :3

[@blackhole3407]

"Good moOOOrning fello mathe - UHGHOUGGHHAAAHH- video" I died of laughter😂

[@PapaFlammy69]

:D

[@blackhole3407]

wow that was quick

[@PapaFlammy69]

indeed :v

[@Thegeektoendallgeeks]

who came back here and watched the video again after this getting referenced in the wikipedia article for the list of integrals

[@giannisr.7733]

0:15 that is the most wonderful intro to a video I have witnessed

[@SlenderCamGaming]

8:02 Ah yes O - O = 0 The three applications of o, O, and 0 fucked with me the entire time

[@PapaFlammy69]

xD

[@VerrouSuo]

bruh they gotta nerf this next patch. and fix all the bugs with 0 and such, but this is OP as heck.

[@PapaFlammy69]

:D

[@angelmendez-rivera351]

That's okay. We were talking in the comments about how t(x) needs to be even for this work. A fair nerf, though the integral is still OP AF

[@noether9447]

@@angelmendez-rivera351 t doesn't need to be even though? We never assumed t to be even. It can be any function.

[@angelmendez-rivera351]

Rohit Tanwar Papa Flammy never made any explicit assumptions in the video about t(x), but the algebraic manipulations he used to simplify the integral only work if t(x) = t(-x). In particular, he inadvertently simplified t(x)^o(x)·t(-x)^[-o(x)] to 1, but this simplification is only valid if t(x) = t(-x).

[@Assault_Butter_Knife]

The integration meta will never be the same

[@baerlauchstal]

This is lovely. (I'm delighted to say, incidentally, that Mathematica handles the integral in the thumbnail!)

[@PapaFlammy69]

:)

[@shototodoroki4636]

The most useful thing I ever found bro... My adrenaline while watching this went 📈📈📈📈📈📈📈 LOVE YOUR VIDS!!

[@PapaFlammy69]

[@jonathannissim2774]

Here before the physicists

[@PapaFlammy69]

ez

[@DavidPumpernickel]

That's true

[@physicsboy1234]

Hey i am a physicist

[@minh9545]

@@physicsboy1234 youre still late

[@physicsboy1234]

@@minh9545 i got first or second comment

[@Ocklepod]

lets start the video with some corona yes

[@PapaFlammy69]

x'D

[@alexandersanchez9138]

Very nice--This is excellent stuff! A truly OP integration technique. It's amazing how powerful symmetry can be in the right circumstances. (Yes, yes, I've already noticed that t needs to be even as well so you guys don't have to tell me.)

[@PapaFlammy69]

:) Glad you liked it Alexander! :D

[@caesar_cipher]

Blackpen showed the exact same technique a year ago : kzbin.info/www/bejne/nXybiJlvj9CNjZY

[@danielburgess7101]

“What the fuck Papa” earned my subscription. Well done sir

[@PapaFlammy69]

[@Kdd160]

7:13 rotating head of James Grime on fire 😂😂

[@PapaFlammy69]

:D

[@VaradMahashabde]

KZbin : an Interesting report you have made there citizen

[@eliseuantonio6652]

How didn't I notice that?

[@Mr_mechEngineer]

How come i haven't derived such a good shortcut. Great work man. Thanks for this.

[@Gqtor]

Thanks for the video! Always love to add another technique to my repertoire. Any chance you could go over Maclaurin Integration? It's new (published this year) and works for every integral as long as there's not a discontinuity between 0 and 2. Maybe you make a sequel to this video like "The Most Overpowered Integration Technique Pt. 2" or something. Anyway, I really enjoy your vids, thank you for the work you contribute to the community! ♥️

[@sunspecies]

YO PAPA this is CHAD mathematics right there

[@PapaFlammy69]

[@Syndicalism]

The intro is top tier Flammy this is a great video. Everything delivered in point!

[@mimithewienerdog6928]

Me about to start hw: 9:22 - 9:24 Me starting hw: 10:14

[@hectorfromthepast5951]

LMAO

[@GelesGames]

Hello from wikipedia

[@ivoryas1696]

Well that's *_one_* way to start a video! Came here from Wikepedia, stayed for the whole thing because I remembered who you were seeing your face and hearing your voice as opposed to seeing you channel name! Kudos ç ✌

[@АлексейРыжков-м9я]

Can't express myself enough, so just thank you so much for the joy of doing maths.

[@PapaFlammy69]

:))

[@VaradMahashabde]

2:16 "Well we are going to have an even function in the numerator and an odd function in the power" I think we all know where this is going

[@PapaFlammy69]

:D

[@meltossmedia]

As an engineer, I didn't notice anything wrong when he said "well e is basically equal to 2"

[@quatsch95]

Hands down the best papa Flammy intro

[@captainchicky3744]

this type of integral actually appeared in the 2023 stanford math tournemant lol and i was able to use this trick to solve it! thanks :D

[@margadbold8222]

man , i love your channel

[@PapaFlammy69]

:3

[@randomcubing7106]

This guy is the pewdiepie in the math community

[@stormtrooperfun2525]

*Pewdieπ

[@ians3930]

Best video in a while, always love the channel

[@PapaFlammy69]

Thx Ian! :)

[@user-wu8yq1rb9t]

I love the concept of this video. I learned how I should think about integrals ( or in general about Math). Great Papa Flammy, Great. I Learned and enjoyed Thank you Papa ♥️

[@jatarokemuri4549]

Papa Phlegmmy

[@Assault_Butter_Knife]

Can't wait to forget about this method during the January exams :P

[@M.Davit613]

Ես ինչ բարդ ձևով ապացուցիր, ավելի հեշտ ձև կա ախպերս:

[@TheJJ65]

i love the enthusiasm here so much

[@demenion3521]

i know, it has been noted a few times already, but t(x) needs to be an even function. the problem however comes when t(x)

[@PapaFlammy69]

Surprisingly it always holds, even if the even function got poles! :D

[@jcfgykjtdk]

Thanks for this video. Extremely interesting

[@Dunga8090]

I love the enthusiasm! Thank you for a nice presentation of an even more nice technique :-)

[@jordanweir7187]

no way dude nice technique, wow always some nice stuff in integration techniques man

[@ranjitsarkar3126]

This guy should get more views and subscribers.

[@PapaFlammy69]

awwwww thank you :)

[@ranjitsarkar3126]

@@PapaFlammy69 😊😊😊 By the way that sound at 0:17 was beautiful and heart touching.

[@thisisnotmyrealname628]

WHo eLSe iS cOMinG frOm WiKIPediA?

[@wanderingpalace]

I don’t see it on my Wikipedia so I am checking it here I think it got removed

[@thisisnotmyrealname628]

@@wanderingpalace NOOOO it really got removed

[@jr_kulik]

This is amazing, I’m in awe !

[@PapaFlammy69]

Glad you enjoyed the video René!

[@calmspace8221]

They say when you round off things you create another reality. That makes that thing variant. ~TVA 2021

[@alberteinstein3612]

This is too OP for my mind to comprehend

[@dijkstra4678]

"Pi is absolutely clickbait, it must work out" -A wise flammy

[@PapaFlammy69]

:D

[@alexisdegivry910]

coolest trick I learnt today, I'll use it if I get a test on it

[@PapaFlammy69]

:)

[@JakubS]

"What a time to be alive!" -Two Minute Papers

[@Ferraco05]

I just rewind and rewatch the intro over and over XD

[@pythagorasaurusrex9853]

Watched the title: WTF!! Watched the video to the end: 😁👍

[@ayushagrawal8198]

this intro is badass

[@PapaFlammy69]

:D

[@ricardoparada5375]

Really cool use of even and odd functions

[@PapaFlammy69]

thx! :)

[@firstnamelastname288]

I had to turn in my lab protocol today and spent the whole day writing this bullshit and drawing graphs. I needed this video, thank you

[@PapaFlammy69]

[@amritbahl1223]

Buddy this is genius

[@PapaFlammy69]

:D

[@durgeshnandinijha6054]

You know, papa, these kind of questions have to be solved within seconds in the JEE Advanced exam. We use something as the king rule.......

[@oofusmcdoofus]

You know you have about 150 seconds for each question

[@talhaabdurrahman9407]

That accent at 3:56🔥🔥

[@abhishekkp7121]

That meme in the beginning gives you the motivation to listen to the entire video. That clock is some next level stuff🔥

[@PapaFlammy69]

:D

[@iamtrash288]

If papa Flammy were a fisherman he would damn well be a fishing magnate

[@PapaFlammy69]

:D

[@lucador977]

There is surely eternity between now and the last time I saw something so beautiful...

[@WhydYouChangeMyHandle]

You should mention that t can be zero since integral is over [-a,a], but use symmetry to do [0,a] (as you did) and then just do (0,a] instead. Not an issue, but I'm surprised you didn't mention it! :) good vid

[@WhydYouChangeMyHandle]

Just kidding, for some reason I thought t was the integration variable xD disregard

[@KNA-m3z]

I have calculus exam later. This is very helpful! Well done Sir/Prof/Ma bui

[@KNA-m3z]

gotta add THIS IS VERY FCKING HELPFUL KEK

[@PapaFlammy69]

:D

[@harish6787]

You fired it really 👑👑

[@WhattheHectogon]

that was so fire that my house burned down...

[@pascaldohr8865]

7:22 - "Same Spiel down here"

[@angrymurloc7626]

t can’t be anything, we assumed it was even during the derivation

[@johnsalkeld1088]

For t to be the same base with -x and x t must be an even function from the proof you gave - but it is nice

[@PapaFlammy69]

yup!!

[@tomkerruish2982]

Instead of e(x) and o(x), you should use g(x) and u(x) for gerade and ungerade. Those terms are used in molecular orbital theory, and that stuff won a Nobel Prize!

[@sidwirb3629]

The proof hurts my brain but it’s too powerful to forget

[@alvinlepik5265]

That's a nice one! Thanks for sharing!

[@PapaFlammy69]

=)

[@neilgerace355]

0:14 Papa gives us the coughin' problem

[@PapaFlammy69]

good one Neil xD

[@huntermills1]

I absolutely love this, brilliance, nothing short!

[@MrRyanroberson1]

funnily enough if you ignore the /5 part, the result would have been more accurate. e^5 /5 ~ 30, which means a guess of 2^5 was spot-on. e / 5^.2 ~ 1.97, which is quite close to 2

[@cubernetes]

This is my new favourite Video!

[@MathIguess]

Best intro so far! :D

[@PapaFlammy69]

:D

[@roeesi-personal]

I'm pretty sure that if t is not a constant it has to be an even function because it has to remain the same when you plug in -x.

[@PapaFlammy69]

yup!

[@lLlILILw]

Oh no... Has it really become possible that parker square is now a meme?

[@manishtripathy5156]

Where's do you get these integrals... although great though:)

[@PapaFlammy69]

Dunno, I come up with many of these out of boredom :D

[@manishtripathy5156]

Is there any website which I can refer to...

[@arturslunga3415]

Wow you are just like my old maths teacher, but with less cursing. :)

[@PapaFlammy69]

watch my older videos :p

[@Phaust94]

Papa, for your comment at 9:24, t can't be ANY function of x, as then you're going to have t(-x), which isn't going to cancel out so nicely in the end.

[@PapaFlammy69]

Yup, it needs to be even! =)

[@NonTwinBrothers]

First vid I saw of yours, good shit

[@hoodedR]

Hey Papa :) Stemerch looks dope

[@PapaFlammy69]

Thx Ranjan! =)

[@Zavstar]

Handwriting was good this time

[@PapaFlammy69]

really? xD

[@deyomash]

what kind of crazy person draws an integral from bottom to top =o

[@pranavsrikanth935]

This is definitely gonna help in my JEE advance exam coming up on 27th september

[@PapaFlammy69]

:) Best of luck!

[@6023barath]

Best of luck!!

[@pranavsrikanth935]

@@PapaFlammy69 thx a ton! Looking out for some more amazing vids like this one X)

[@pranavsrikanth935]

@@6023barath thankyou!

[@vikiv.1352]

Here before the Internet Historian

[@gamingadda901]

10:21 my reaction when I first saw this integral

[@huh.6149]

10/10 intro **inaudible screaming**

[@PapaFlammy69]

xD