Evaluating an absolute Monster - Coxeter's Integral

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Ahmed's Integral: • A Savage Integral! Eva...
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There we go! Let us tackle this absolute bad boi today! This has been my longest video session ever an is atm the longest video on this very channel! Enjoy the show :) I tried my best explaining everything as good as possible =)
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[@quahntasy]

43 minutes of monster slaying. Am I in a dream.

[@tgeofrey]

Animetor email me at [e-mail]

[@denverelisha7878]

I realize I'm kinda off topic but does anybody know a good place to watch new tv shows online?

[@gregoriousmaths266]

i see arccos in a derivative, i moan slightly i see arccos in an integerahl, i have a mental breakdown

[@parthpawar7837]

41:15 Ahmed's Integral! Top 10 anime cross overs, that was really surprising

[@FICHEKK]

Hey man, I know you love to solve these crazy integrals, but have you ever considered making a series in which you teach people to integrate, starting from the basics and building up the difficulty as the series goes on? Regardless, you are great and keep going!

[@benmorton3153]

I agree with this statement!!!!!!!!

[@coycatrett2303]

that would be flammtastic

[@AayushBatra]

Yes please make it!!

[@ericthegreat7805]

Yes pls

[@melaniem2965]

I think he should teach advance integration, but if we’re talking about integrate x^2 + 2, There are many channels for that

[@Swimmer7596]

Lol at "Can we trust the Peano Axioms?"

[@u.v.s.5583]

I don't trust a shady Italian. I only trust my accountant. If he tells 2x2=5, then 5 it is.

[@46pi26]

KZbin: "Alright Papa I know you're starving so here are 7 ads just make sure you're family friendly" Papa Flammy: *skullfucks a monster integral* KZbin: oof

[@anegativecoconut4940]

There is no nice cancellation in the wild. Papa's just taught this to you.

[@SuperSilver316]

that moment when you you are doing so many transformations, that I forgot what integral we were doing

[@wherestheshroomsyo]

29:57 literally hand waving argument lol

[@akshaypr9164]

Good job! ..Yes you can interchange the integrals due to the tonelli's theorem..notice that your integrant is a positive quantity(luckily!!) and also it turns out to be continuous(very lucky), hence is a measurable function( wow!!) hence you can interchange the integral signs.

[@3manthing]

My respect for not losing your shit filming this video, calculating stuff in your head all the time.☺

[@PapaFlammy69]

:3

[@Melanie12047]

40 min of integration MY DREAM CAME TRUE😍😍❤❤

[@neilgerace355]

11:37 No, I can't. This time I would like you to prove 2 x 2 = 4 please.

[@maximilianmueller4707]

Sometimes your equal sign looks like a minus sign

[@atrimandal4324]

37:24 :') Good old days of Fappable Maths 41:15 Wtf dude that was crazier than most crossovers 😍😍 Hey, random week 2.0 was great

[@atrimandal4324]

Flammable Maths Find me one person who didn't 😂😂

[@fabfin5814]

dem engineer bois already attracted :b

[@atrimandal4324]

FabFin Dude, I'm a med student and I'm addicted to Maths partly because of this channel. Show this to a Lib. Arts guy and he'd be attracted too😂😂

[@Kuratius]

"Cocksetters integral"

[@fabfin5814]

Jim Moriarty whatever you want to tell me with that, I agree.

[@weerman44]

Amazing man. Really love this channel

[@danielesantospirito5743]

I came back to watch this video a second time to "train my attention", trying to watch it from the beginning to the end without losing any passage. It's a very nice and difficult integral, I really admire the fact that you don't use notes, I think I would not be able to remember such a procedure without doing it many times.

[@reydavid7300]

I just started the video. This is above 43 minutes log but long time ago I knew a mate that evaluated this integral by exchanging "2cos(x)" for "tcos(x)" the he took the derivative of the whole integral with respect to t, made some cool simplifications then integrated with respect to x, uterly, he integrated with respect to t and found the constant.

[@karineaudet6270]

Woo.

[@bryantwiltrout5492]

Great pun! “De-phi-ing” I laughed out loud at that. Well done sir!

[@jfb-]

You can justify interchanging the integrals by Tonelli's theorem, which allows you to interchange integrals where the integrand is non negative

[@azmath2059]

This is just flamin' unbelievable !! What you are doing here requires great skill and discipline considering that your lecturing from memory without notes or cue sheets. Well done!!

[@hridayansh7682]

i was like yeah... i can give it a shot "took the paper, writing the question.... mid way of writing question..... No I can't."

[@TheRedAnvil40]

I have ZERO idea what was going on, yet I watched a 45 min math problem and now I legit feel bad for him. This is WILD.

[@TheRedAnvil40]

He could have written anything and I would have believed it.

[@PapaFlammy69]

:DDD

[@leroyzack265]

This was an absolute monster and you did a monstrous job. Really I rank this integral as one of the taughest. 🎉🎉 I really love this one it was awfully amazing.

[@Saki630]

Gauss did this for fun and Fermat executed this in 13 steps but could not fit it all into margins in Gauss's book.

[@grant1390]

That would also involve time travel.

[@danieleferretti9117]

You can exchange the integral signs because of the Fubini theorem: you are integrating a positive function, so you can do that

[@Cubinator73]

The big f'n square root at 8:55 really made things easier...

[@jemcel0397]

You really showed Math is fun

[@jemcel0397]

Flammable Maths always ;)

[@yogitshankar6348]

His style makes it way for interesting

[@Invalid571]

Sees notification, clicks on video, sees it's 43 mins long, closes video. Syke, I watched it all! XD

[@ManmohanSingh-tv2tb]

It really means for me when solution of integral appears after 1 hour.Great

[@u.v.s.5583]

Papa's theorem. Every function from R to R is integrable in elementary functions. Proof: Come on!

[@nanaeK]

Coxeter got torched. Well done paypay flemmy

[@parthpawar7837]

Press F to pay respect.

[@lukamitrovic7873]

F

[@ricksanchez3035]

F

[@shambosaha9727]

ma

[@AA-gl1dr]

F

[@SSS20025]

F

[@danrain12345]

Honestly I watch so many videos where people pronounce it “zed” that I now do it lmao

[@someperson9052]

Are you American?

[@shambosaha9727]

Zed is perfectly normal

[@flutterwind7686]

Welcome to Canada

[@danielwalker2381]

4:12 my OCD went crazy x-----------------------x

[@Miaumiau3333]

my wrist's gonna hurt tomorrow

[@ClaytonMurzyn]

Dude this was sick! Your algebra is crazy

[@lukamitrovic7873]

HOLY CRAP 45 MINUTES

[@purecalcium354]

I don't really know how to integrate properly, but god damn that was fun to watch.

[@himanshumallick2269]

I'm glad you made a video on the first integral posted on that 'artofproblemsolving' page. Waiting for more.....

[@himanshumallick2269]

@@PapaFlammy69 This one: artofproblemsolving.com/community/c7h1674162

[@adityavarma193]

I've been doing one MIT integration bee integral a day. I'm not able to solve every one, but I seem to be getting better when I analyze the solutions if I didn't know how to do that integral. It's a tough life...

[@didyoustealmyfood8729]

bruh when he pulled that ahmed integral out i was like *surprised pikachu face*

[@PapaFlammy69]

:D

[@brammiddelkamp1861]

When you realize the nummerical solution is calculated within a minute and gives the same result

[@user-qu6xz4uv3l]

同級生からこの問題を出されて解らず困っていたので助かりました。 thank you so much!!

[@Harkraft]

My god this is the best thing that I ever seen in my whole life cheers to you man

[@ritabratanag1821]

Thank you sir for solving one of the best and magnificient integral which finally terminates into the Ahmed integral

[@louisthirion8179]

Same Spiel down here😂😂 8:18

[@ivancheems35]

I watched rick and morty so I could follow every step of this integration papa

[@Czeckie]

31:30 pappa, you've interchanged the integrals long before this point even though you didn't write it up.

[@Ricocossa1]

That's the final boss of integrals.

[@cafeinst]

This is perhaps the most interesting math channel on youtube.

[@dharmanshah1239]

Ohh monster boi!!Thank god finally ...

[@dharmanshah1239]

Ikr..

[@dharmanshah1239]

Jokes apart Jens you are definitely my inspiration to make my own channel in future..Thankyou!!

[@kshitijkayastha]

Can you please make videos on solving differential equations using Laplace Transformation (and then inverse Laplace)

[@Setiny]

I can’t solve the integral - Panic There’s a video about it - Calm 43:13 - Panic

[@Sokobansolver]

I can't solve the integral - Panic There's an online integral calculator with steps - Calm "The calculation was aborted because it took too long." - Panic

[@lukamitrovic7873]

Who dislikes this wtf?

[@Gold161803]

If I were to dislike it, it would be because of the ridiculous number of ad breaks.

[@ifteharulhaque2600]

@@Gold161803 it's a 40 min vid so it's fair

[@Gold161803]

@@ifteharulhaque2600 Not really. Every other 40 minute video I've seen has 2 or 3 ads, and maaaaybe a fourth at the beginning or end

[@gregoriousmaths266]

hehe 69th like

[@didyoustealmyfood8729]

papa flammy is gonna haunt those who dislike this masterpiece

[@danielkirilov8065]

FUUUUU, finallyyy de 40min intigril :^* Sugoi papa.

[@ChibiSheepy]

The most fabulous 43 minutes of my life

[@hubomba]

That was inspirational. I was in awe of the size of this lad. Absolute unit.

[@duncanw9901]

At 9:30 I just used the triangle thing. Absolutely no idea what you were doing there lol but I got the same thing :)

[@JohnAbreu17]

I'm loving this organized chaos.

[@dectorey7233]

Why doesn't this have enough views? This is fire

[@jamez6398]

Holy fucking shit! 45 minutes!!?? Damn... That is one hardcore integral...

[@cesaraugustogilacosta5336]

Nice integral. It's useful to practice for some calculus tests. Continue like this man.

[@michaelempeigne3519]

interchanging the integral signs is called fubini's theorem

[@gesucristo0]

Really impressive man...Could you evaluate 1/3 factorial? Using Γ i showed is equal to int from 0 to inf of e^-x^3 but the i don’t know how to continue

[@mithsaradasanayake3211]

Seeing whether this has a complex answers or we could call in quaternions

[@George-ij2gm]

Whenever you phase in from the left side of the screen, I got lost. 😂😂😂😂

[@PapaFlammy69]

xD

[@shanmugasundaram9688]

You do this integral in the style as Andrew Wiles solves Fermat's last theorem.There may be easier way of doing this integral.Anyhow the proof is quite interesting.

[@dgrandlapinblanc]

absolutely crazy. Thank you.

[@balakumarank2006]

Imagine If this integral is in your compulsory 5 mark question 🤪

[@Sokobansolver]

Meanwhile here I am still having not learned how to compute derivatives or antiderivatives of inverse trig functions. This seems like the final boss of integral problems.

[@temurson]

Okay Papa, I give up. It is 33:01 and my brain turned off. I think that's too much for me xD By the way, I think you should have had 8/sqrt(3), not 8*sqrt(3) at this point (I am not sure though). Thanks for your sacrifice (I cannot call this video anything else)

[@temurson]

Apparently, your brain did not last much longer than mine xD 39:55 Papa's machine going offline

[@thethug1946]

That was truly a coxeter integral

[@neb8167]

amazing

[@juli099]

Increible, fantastico, asombroso......

[@strikercompact2847]

You know... You mad man. I love u

[@VALIANT_Electronics]

Sometimes it is difficult to understand some steps in your videos, but after investigating I can understand them a little, for this reason I would like to know if there is a list of topics that we need to know in order to fully understand all the steps when you solve those spicy bois and those beach bois integral's in your videos. I am a second semester student of electronic engineering, I know the differential and integral calculus also linear algebra and a little bit of multivariable calculus. Greetings from Valledupar-Colombia. Thank you

[@danielfong2315]

next random week when? :'(

[@PuzzleQodec]

22:30 So you _think_ you gpt rid of the 3.... but in reality it hid under the pi.

[@PapaFlammy69]

bruhv

[@Idk-hp3oo]

#Hard 2 swallow pills:This Integral.

[@debjitmullick7004]

Such a fascinating video .... But what was the book in your hands 0:19

[@tszhanglau5747]

Nice way to end this random week. When will be the next random week?

[@CT-pi2gl]

Need to append the Ahmed integral video into one video for completeness!

[@Sokobansolver]

Calculus: Kaizo edition

[@shimuzeisusu]

At 23:40 shouldn't the upper and lower bounds change with a change in variable from t to \phi

[@gregoriousmaths266]

uwu ahmed's integral at the end! That was unexpected

[@markos1623]

Imagine if the camera ran out of battery and he didn't notice...

[@yoav613]

you laugh you integrate and then you cry... poor andrew dotson

[@Mot-dh5sx]

I was watching this at 3 am and accidentally fell asleep while watching. idk

[@dannygjk]

NO! (holding ears) la la la la I can't hear you! la la la la...

[@dagatho]

Papa you're insane, how do you come up with this sorcery? Fucking insane

[@user-ke2bz8xh1l]

You are my hero! BTW, are you Australian?

[@rakhimondal5949]

Holy shit it's not a family channel

[@shaqramento3238]

That's your masterpiece

[@MagnetThunder3528]

Sorry I don't understand where the 2x disappears to in the expression at 4:13. Does it just happen to equal 0 through the variable substitutions or is there another explanation?

[@ricardofranco7419]

Hmm it’s been a while but can we not use complex analysis to do this integral and make it be less steps?

[@michaelempeigne3519]

at 29:00, you did not put (x^2 + 3 ) in the denominator when doing the substitution of 1 / ( 1 + u^2 )

[@dasharethra8981]

When he said he was stupid, me be like wtf!!!!!

[@abdullahalmasri612]

Yeeeee I'll stick to my calculus 1 exercises for now thx

[@shimuzeisusu]

Can we really assume cos (t) / sqrt ( 2 - 3 sin^2 (t)) as a constant?