A pretty awesome integral! Exploiting some symmetry bois [ Papa Flammy's V2 ]

[@torresko211]

The 4th link (unique decomposition) is not available, anyone else tried and didnt work?

[@torresko211]

Thank you mah boi

[@restitutororbis964]

Flammable Maths Uh papa do you know where I could see the 2nd video? Its not working either and it looks like a neat technique.

[@bishopjared1078]

you prolly dont give a shit but if you are stoned like me during the covid times then you can watch pretty much all the latest movies and series on instaflixxer. Been binge watching with my brother for the last couple of months :)

[@lukemarc5890]

@Bishop Jared yup, have been watching on InstaFlixxer for since december myself =)

[@h4c_18]

That integral was brutally murdered

[@mattgsm]

DV just like England with football

[@kuravasic]

Can’t wait to see “10 ways to integrate cos(x)” 👌🏻

[@eSit0]

ja dann hau mal raus, haha ;D

[@khemirimoez8661]

Lol boi you had it coming

[@thelightningwave]

It's now at 22 or something, because of Mathvengers.

[@brandonklein1]

That function decomposition into an odd and even part is a really powerful tool.

[@bartoszwojtowicz8770]

You are one of the reasons I started to love maths so much in the last 12 months. Now I'm changing my degree to Math and Statistics this October

[@ethanmartin2781]

papa flammy's technique > papa Feynman's technique

[@OkItHappened]

I need to take more notes in my Discrete Meme Theory class

[@amitdeutscher7448]

That was so beautiful. Almost... almost if it was planned all along :O

[@CreativeStyled]

This was dank.

[@reeshav4955]

This channel is straight up amazing

[@koenth2359]

Great technique, that will tame the beasty boi. Must remember that one, I would never have come up with it. From 3:00 onwards pretty straightforward, could write ahead of the video.

[@holyshit922]

Integral can be calculated in following way limit (sum(cos(ξ)dt_{i}),max(dt_{i})=0) dt_{i} - length of subinterval of [0..x] ξ - is the value from subinterval [t_{i}..t_{i+1}] To avoid calculation of infinitely many values we can use theorem that for continous functions value of this limit is independent from interval divisions

[@lorenzoloi6436]

you're so high

[@rafaellisboa8493]

high on maths

[@ciarfah]

Ginger Stalin maths is a gateway drug to engineering. Join me.

[@gregoriousmaths266]

No

[@melaniem2965]

No, engineering is a gateway drug to physics, and physics is a gateway drug to math

[@melaniem2965]

I started with Zach Star, which led me to physics, which led me to blackpenredpen and flammablemaths

[@ethanjensen661]

The production quality keeps getting better. Good work.

[@hue_huebilachbitteubermein5208]

5:46 and integral war was born

[@cedricr.9102]

Quiet difficult way for a representation of the integral of cosx

[@mipmip4575]

1:45 isnt the dx missing for the first integral? Also awesome video :) With another powerful tool like this the battle against integrals is heating up xD

[@dai2dai246]

THIS IS LIT AF

[@vincentcjs]

This is beautiful

[@mrflibble5717]

Beautiful Solution!

[@sproutssupport7789]

This Integral are so easy to understand,i and easy to remember

[@carlosvargas2907]

So much nostalgia... You dirty old boi...

[@TheCEMF]

That's a beautiful boi right there, thanks for the video

[@nuranichandra2177]

This method is popularly known as ‘Taming the monster’

[@cicik57]

wow it is really cool trick. multiply on e^(-1/x) and swap x and -x when cos remains the same since cos(-x) = cos(x) you end up that the same integral is in form of e^1/x * cos(x) / -.-. then you add both versions of the same integral having 2I = integral of just cos(x)

[@mohandoshi153]

Papa - you simply rock. Keep it going Papa.

[@ThePron8]

papa Flammy never lets people down!

[@tatjanagobold2810]

Oh ja das video mit 10 arten des cos(x) zu integrieren klingt echt wie eine lustige idee😂

[@angeld3]

Integrate x with 10 different methods😃

[@herowise6021]

Its a good rom com must watch

[@rayvianasampaio379]

I understand very well why this very young german Professor Scholz earned the mathematical Fields Medal !!!! Congratulations !!! From Brazil . Ray Viana Sampaio .

[@user-wu8yq1rb9t]

*Papa I miss you and your great Flammable Math* *Please be more active, Papa*

[@srpenguinbr]

I did it in a similar way. I broke it into two integrals, one from -pi/2 to 0 and another one from 0 to pi/2. In one of them, I made the substitution u=-x. Then, I used dummy variables to add it back to the other integral and then some stuff canceled out very nicely.

[@MaxxTosh]

“I should make a video on how to do this integral, I could probably come up with ten different ways.” TOP FIVE FORESHADOWING MOMENTS OF THE 2010S!!!

[@thomasblackwell9507]

Yes do the Integral 20 different equals!

[@srikanthtupurani6316]

nice. can you make a video on finding volumes? i was trying to solve a problem in brilliant it was related to volume of a canoli. i ended up with some integral which i could not evaluate. there are some interesting applications of fubini's theorem in calculating double integrals.

[@thelightningwave]

The integral that started Mathvengers. I wonder what is going to be in Euler's game. Hopefully all of the mathvengers go back in time to stop Jens from killing this integral.

[@slavinojunepri7648]

Amazing solution! And this mathematician is as funny as hell.😂

[@marcinsosinski7740]

Mind blown!

[@wiloux]

a little problem for papa flammy : a/bc + d/ef + g/hi = 1 («bc» notation is not b times c but a number with 2 decimals like 65). You must find a,bc,d,ef,g,hi such as a/bc + d/ef + g/hi = 1

[@OneShotKill711]

that was so satisfying omg

[@restitutororbis964]

* S P I C Y B O I*

[@akashnarayanan9750]

yo what's the music for when you have the problem displayed at the beginning? it's so good! Also, keep up the great work man, love your videos!

[@ciarfah]

3:58 "bei Gott", otherwise known as with papa Flamy

[@holyshit922]

In Fichtenholz is similar decomposition for R(sin(x),cos(x)) integrand

[@Nivesh26]

f(x) from a to b = f(a+b-x), we can solve this with this method within 3 steps i think

[@skamaralesso363]

Thank you, daddy. Give me more.

[@sab1862]

H...... How?!

[@bishbash111gb]

There was an easier way to combine the fractions than you did. If you multiply through the e^-1/x + 1 term by e^1/x you get obtain e^1/x on the numerator and 1 + e^1/x on the denominator. You can then add the two fractions together and obtain it all being equal to one.

[@informationparadox387]

It's one of the most popular definite intigration question type in JEE Mains!👽

[@ShanBojack]

fuck JEE

[@whebon7266]

This function jumps from 1 to 0 at x=0. It seems like you can just add up the areas of [-pi/2, 0> and

[@avtaras]

Hey papa, I know this request of mine will probably not be the most popular one but- Do you think you could make some of your calculus / linear algebra / trigonometry videos in German just like blackpenredpen does in Chinese (his own language)? Haha it’ll be very useful to Germans in your country who don’t speak English that well (if this subset even exist lmao) but I am mainly concerned about this: It’s summer now, I am nearly finishing my exams and want to get back to studying German, while also practicing my favourite hobby on my favourite channel 🥰 Also, whilst my knowledge of daily life German is pretty dayumn good, I consider moving to Germany in the future and if I ever do, it’ll be imperative to know some dieustshc =P

[@Henrikko123]

Danke, Vater

[@reinerwilhelms-tricarico344]

Wer hätte das gedacht! Cool.

[@Enslex]

That was beautiful... even though I don't know how to integrate...

[@the_martian_45]

Oh my. I never knew Papa was a symmetry boy.

[@46pi26]

I'm officially a patron Papa Flammy; keep up the good work!

[@46pi26]

Flammable Maths definitely a video too!

[@46pi26]

Flammable Maths just won't be able to submit one in time for flammyday :/

[@augustinfrancotte3163]

love it

[@raylee1222]

papa is so amazing

[@jlxip]

I love this channel.

[@theskycuber4213]

One of the best you have done! And guess what, everything was formal lol.

[@elfaroukharb3979]

By the way, KZbin hasn't been notifying me of your videos even though I have the notification bell on. I wondered why you hadn't uploaded in a while and checked your channel to see you already uploaded 2 videos!

[@vangrails]

But I assume we can generalize this? We can replace e^(1/x) with any f(x) as long as f(x)*f(-x)=1 ? Can we for example replace e^(1/x) with e^(sin(x))?

[@MCMCFan1]

Please show that sin(x) =sin(x+2Pi) with the taylor series of sin. Ps thats an absolute beast ^^

[@joao_pedro_c]

I would love to see 10 differents ways to Integrate cosine, pls do it!

[@sombal1999]

Papa Flammy isn't there a problem with this integral cause f(x) isnt continuous at 0?

[@sombal1999]

@@PapaFlammy69 f(x) isn't continuous but then f(x)+f(-x) is! What is this witchcraft

[@許祐承-k5y]

what the amazing identity it is!

[@torresko211]

Awesome video as always

[@jimnewton4534]

wow! nice development.

[@atharvas4399]

at 3.00 how do you know that the integrand is even?

[@timdedecker7894]

'What the fuck are those?' ~not your average math channel

[@IronMaidenEE]

How can you integrate a function that is not defined in an interval? f(x) is not defined at x=0 and therefore not continuous. How can you integrate a function that is not continuous?

[@ryanmuller9497]

Integration is pretty chill about this sort of thing - probably the most extreme example is the unit impulse function, which has a zero value everywhere other than x=0, and is infinitely large at x=0, such that the integral across any interval that includes x=0 is defined as being equal to 1. To think about it more formally, there are two useful things that can counter the infinite effect of the discontinuity. Firstly, an infinitely large value times a differential element approaching zero can on its own converge towards a finite value if the function approaches infinity slowly enough. Secondly, a positive infinitely large value can cancel out a negative infinitely large value under the right circumstances. I'm not quite good enough with formal calculus to know which of these allows the method used in the video, so I'd welcome input from other comments, but I do know that integration typically copes relatively well with discontinuities in functions.

[@mortezamodarres2470]

At x=o e^1/x is infinity. Cos(0)=1 then 1/e^1/x +1=1/infinity which is zero. It is well defined at x=0

[@andreochimal1077]

Mathvengers was born this day

[@moskthinks9801]

1:44 you missed a dx. Good remade vid tho.

[@moskthinks9801]

Flammable Maths you're welcome, lel

[@terveloc]

What did you observe about this integral that led you to try odd/even decomposition? What led your intuition?

[@itsrush8496]

Wolfram alpha doesn't have papa's technique :(

[@tulgatbolderdene7493]

4k Mathematics DOPE!

[@sweetpotato_35]

You could just substitute u=-x and add the two equal integrals together. This is more straightforward and instructive I think.

[@jbermudez01]

How can you say the symmetrical integral of the odd function is 0 if the function isn't continous on [-a,a]?

[@charlievane]

Thanks

[@domenicogrimaldi591]

I plugged this into an integral calculator and got "No antiderivative could be found within the given time limit, or all supported integration methods were tried unsuccessfully." lol

[@PapaFlammy69]

:DDD

[@ArchyBold-mu5kq]

Well, this happened probably because integrand is undefined in 0

[@jms547]

Daddy daddy can u gimmie some integrals with Bessel functions? I promise to be good!

[@aminegaming1998]

beautiful mind

[@Walczyk]

great stuff my boys

[@gustavorochavillela6323]

Complete S U C C ess

[@neo_tsz]

The title is true. I'm pleased.

[@amarsuljkic60]

Moin Flammy, was studierst du? Mathe im Bachelor oder Master? Einen schönen Tag dir noch!

[@tgx3529]

This is very interesting

[@PapaFlammy69]

:)

[@rohitg1529]

Do u-substitution: u=-x The same thing happens

[@rekyller1]

Isn't it integral from -pi/2 to pi/2 ? how did it become from 0 to pi/2 ?

[@MrMelkorbaggins]

so the next time someone asks "what is a 1?" they'll get this

[@strengthman600]

Now that's nice

[@Gold161803]

You've got me shouting at my screen

[@atpugnes]

This function is discontinuous at 0. Will that be a problem?

[@destroctiveblade843]

using the substitution t=-x also works well

[@im_Smitty]

Holy shit bamboozled again

[@im_Smitty]

Flammable Maths Like every step makes so much sense but to think of this method man jesus H

[@tomwu163]

OMG 5:59 is foreshadowing the fapmas present from papa!

[@rahmouniabdel3298]

Genius !

[@franciscoabusleme9085]

Astonishing

[@ivekhd4764]

Whenever i see your face, it's automatically good day :)