Integrating the boi of your Putnam dreams ( Sophomore's dream: Integral x^-x from 0 to 1 )

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  • เผยแพร่เมื่อ 23 ธ.ค. 2024

ความคิดเห็น •

  • @gaetanramos7903
    @gaetanramos7903 6 ปีที่แล้ว +1749

    > assuming you can interchange integral and sum signs without proving it first
    REEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

    • @PhilGarmann
      @PhilGarmann 6 ปีที่แล้ว +219

      Flammable Maths By Tonelli’s theorem you can interchange the integral and the sum since your integrant is ≥0 on the interval you’re calculating the integral over ie. [0,1]

    • @RadicalSolver
      @RadicalSolver 6 ปีที่แล้ว +81

      Philip Garmann
      LOL
      The main property required is that the integrand is integrable on every compact subinterval of the open half-line (0,\infty).

    • @GaetanAlmela
      @GaetanAlmela 6 ปีที่แล้ว +29

      Hey we have the same first name :D

    • @davidkippy101
      @davidkippy101 6 ปีที่แล้ว +42

      It's very intuitive because integrating a sum lets you split it into several integrals of each component of the sum. Then you can just sum up the integrals.

    • @ninakoch1799
      @ninakoch1799 6 ปีที่แล้ว +17

      It‘s trivial😂

  • @TheGamer583
    @TheGamer583 6 ปีที่แล้ว +1334

    This is actually pretty amazing, because 1/(j^j) is essentially j^(-j), which is practically what we started with, x^(-x). So theoretically we converted a continuous sum (the integral) into a discrete sum of literally the same form! But instead of 0 to 1, we have 1 to infinity.

    • @PavelSTL
      @PavelSTL 6 ปีที่แล้ว +208

      I wonder if this fact can be used to show that the set of real numbers is bigger than the set of natural numbers (instead of Cantor's diagonalization proof)

    • @RadicalSolver
      @RadicalSolver 6 ปีที่แล้ว +31

      TheGamer583
      Why don't you try doing a Riemann Sum computation of this integral?

    • @kichveellc275
      @kichveellc275 5 ปีที่แล้ว +23

      =1.29129

    • @josephgrossenbacher7642
      @josephgrossenbacher7642 5 ปีที่แล้ว +4

      @@PavelSTL , a look at "the Hilbert hotel" ( &/v at "the hyperwebster" ) will give you a negative answer ... !!!

    • @intfxdx
      @intfxdx 5 ปีที่แล้ว +14

      Wonder what other functions have \int_0^1 f(x) dx becoming \sum_{j=1}^\infty f(j) :) Great video Flammable Maths!

  • @benjamincalloway
    @benjamincalloway 4 ปีที่แล้ว +431

    Sorry sir, I couldn't hear you over the sound of my engineering approximations

    • @gregoriousmaths266
      @gregoriousmaths266 4 ปีที่แล้ว +1

      Mr. Skeltal hahahaha

    • @Dawatehaq786
      @Dawatehaq786 4 ปีที่แล้ว +1

      Trigonometry for AS and A level th-cam.com/video/-WzZRx4vVxI/w-d-xo.html
      Watch and share and subscribe our channel

  • @oliverhees4076
    @oliverhees4076 6 ปีที่แล้ว +744

    Drinking game: take a shot anytime he says "boi" or "boiz"

    • @mcmage5250
      @mcmage5250 6 ปีที่แล้ว +7

      Oliver Hees j dond ghe vhallenve alr2adg it went fins i fhink

    • @redaabakhti768
      @redaabakhti768 6 ปีที่แล้ว +10

      you ll solve riemann conjecture but only drunk people will understand you ll forget the solution when sober

    • @redaabakhti768
      @redaabakhti768 6 ปีที่แล้ว

      this is your destiny

    • @alsoeris
      @alsoeris 5 ปีที่แล้ว +3

      Crack open a cold one with the boiz

  • @tissuepaper9962
    @tissuepaper9962 6 ปีที่แล้ว +354

    "Infinity boi" is now my new favorite phrase

  • @jony7779
    @jony7779 6 ปีที่แล้ว +594

    Who would win? The proof of Fermat's Last Theorem or
    O N E I N F I N I T I B O I

  • @g0rgth3b0rg
    @g0rgth3b0rg 6 ปีที่แล้ว +251

    I love when the Gamma Function pops up in these crazy integrals.

  • @46pi26
    @46pi26 6 ปีที่แล้ว +999

    Infinity bois are the best bois

  • @nenume00
    @nenume00 6 ปีที่แล้ว +560

    wait wtf memes and maths?

    • @notsojharedtroll23
      @notsojharedtroll23 6 ปีที่แล้ว +49

      This boi is the only English speaker boy that uses the pacman :V
      Kudos from Mexico xd

    • @general_prodigy
      @general_prodigy 4 ปีที่แล้ว +1

      It's like oil and water, or rather a poly protic compound and a non-polar compound
      Chemistry bois will know this

  • @drpeyam
    @drpeyam 6 ปีที่แล้ว +386

    For people saying that this video is on my channel: I promise you that we came up with this idea independently a couple of weeks ago, it’s just a pure coincidence that our videos got uploaded almost on the same day!

    • @jeromesnail
      @jeromesnail 6 ปีที่แล้ว +8

      Dr. Peyam's Show haha I was thinking "I already saw this one". You should have made it in German ;p

    • @michaelempeigne3519
      @michaelempeigne3519 6 ปีที่แล้ว +2

      Can you do a video on nonlinear PDEs ?

    • @porter_moody
      @porter_moody 6 ปีที่แล้ว

      i dont believe it

    • @djameleddinekebiche1268
      @djameleddinekebiche1268 6 ปีที่แล้ว +64

      Oh boy here we go again, it's the Leibniz-Newton controversy again.

    • @MrAzizomer
      @MrAzizomer 6 ปีที่แล้ว +2

      calculate for me the probability of that happening

  • @SimonClark
    @SimonClark 6 ปีที่แล้ว +560

    This was fun! You're a natural teacher - I look forward to seeing what you will upload in the future!

    • @potatopassingby
      @potatopassingby 6 ปีที่แล้ว +4

      hello simooooon :D i have no idea how i found your comment in this video, it was randomly recommended to me lol

    • @MoJohnnys
      @MoJohnnys 6 ปีที่แล้ว +9

      I sense fanfiction probabilities...🙈

    • @soyoltoi
      @soyoltoi 6 ปีที่แล้ว +8

      Top 10 anime crossovers

    • @Neo-br3uc
      @Neo-br3uc 6 ปีที่แล้ว

      Ohhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh myyyyy

    • @alexandernissen4353
      @alexandernissen4353 6 ปีที่แล้ว +1

      I agree dr. Clark!

  • @chriss6356
    @chriss6356 6 ปีที่แล้ว +286

    commuting an infinite sum and integral without hesitation *im shook*

    • @elfaroukharb3979
      @elfaroukharb3979 6 ปีที่แล้ว +86

      My real analysis professor would've had a heart attack seeing this.

    • @hansenchen1
      @hansenchen1 6 ปีที่แล้ว +19

      and +Elfarouk Harb: This could be proved using the Fubini's theorem.

    • @WhisDragonBallSuper
      @WhisDragonBallSuper 5 ปีที่แล้ว +3

      @@hansenchen1 he should have atleast written it

    • @chihebsaidi2054
      @chihebsaidi2054 4 ปีที่แล้ว +1

      @@hansenchen1 Elaborate please

    • @stephankarl1301
      @stephankarl1301 4 ปีที่แล้ว +14

      @@chihebsaidi2054 Der Beweis ist dem Studenten als Hausaufgabe aufgegeben

  • @bartoszwojtowicz8770
    @bartoszwojtowicz8770 6 ปีที่แล้ว +111

    Now that's the 'recommended for you' I was hoping for

  • @GeodesicBruh
    @GeodesicBruh 5 ปีที่แล้ว +90

    When I’m faced with a hard Integral I usually just call the integrand f(x) and then I say let F(x) be the integral of f.
    I don’t know why you guys use these “techniques of integration”.

    • @isaacdeutsch2538
      @isaacdeutsch2538 4 ปีที่แล้ว +26

      And here we have a physicist

    • @godson200
      @godson200 4 ปีที่แล้ว

      It is a standard method of solving...what you said... I.e we take F(x) is the integral and then simplify... We have a whole chapter of 45 pages on it

    • @davideranieri5553
      @davideranieri5553 4 ปีที่แล้ว +16

      That actually does happen e.g. the special functions of analysis. Realize you can't find the antiderivative of say 1/ln(x)? Slap the name li(x) on it and call it a day

    • @appa609
      @appa609 4 ปีที่แล้ว +9

      Exam: Find the solution to this equation
      Me: Def: x a real number such that it satisfies this equation.
      x is the solution.

    • @k_meleon
      @k_meleon 4 ปีที่แล้ว +2

      @@appa609 well that's kinda what the root is in a sense. sqrt(n) is the positive number x such that x^2 = n

  • @evanbelcher
    @evanbelcher 6 ปีที่แล้ว +34

    This was fun to watch. When he did substitutions so it fit perfectly into the gamma function template and things started canceling out I was blown

  • @janderson2709
    @janderson2709 6 ปีที่แล้ว +126

    This is how good I want to be one day.

    • @FiremarkPl
      @FiremarkPl 11 หลายเดือนก่อน

      Hello, im from future! Have you achieved the goal?

  • @badjumpcuts6599
    @badjumpcuts6599 6 ปีที่แล้ว +85

    I laughed.
    I cried.
    You, sir, are an artist

    • @sansamman4619
      @sansamman4619 6 ปีที่แล้ว +8

      BadJumpCuts, it's called modern art.

    • @RadicalSolver
      @RadicalSolver 6 ปีที่แล้ว

      Imprecision is art?

  • @zachydrogeo
    @zachydrogeo 6 ปีที่แล้ว +19

    this video is making me relive uncomfortable traumatic experiences from calc 2. so glad I'm in the cozy arms of simple calc 3

  • @1anya7d
    @1anya7d 6 ปีที่แล้ว +115

    the BOI

  • @mounodeepchakraborty3190
    @mounodeepchakraborty3190 6 ปีที่แล้ว +14

    Papa Flammy, your way of explaining math problems is very unique and it goes straight to the head !! your attitude and way of explaining things is so cool and I never get stressed out.. wish I could get teachers like you in my graduation !! 😊😊😊

  • @Yatukih_001
    @Yatukih_001 6 ปีที่แล้ว +1

    Why thank you!!!!!The mathematics channels are among my favorite youtube channels. Enormous amount of truth there!!! Amazing work and really well done and wishing everyone the best!!

  • @Crustyislooking
    @Crustyislooking 4 ปีที่แล้ว +22

    Me after finishing AP Calc: Damn I can finally watch videos on calculus and know what’s happening.
    Nvm

  • @quantumchill5237
    @quantumchill5237 6 ปีที่แล้ว +150

    Putnam memes for Sophomore dreams

  • @Storm-wk8hy
    @Storm-wk8hy 4 ปีที่แล้ว

    I clearly have no words to appreciate you......i was like the type of person who hates integration the most....but the way u approached each and every questions bloomed up an interest in me to see more of ur videos....u really changed me a lot...i dont know whether you will see this comment or not...but im proud to say u r my frst subscriber related to MATHS...thumbs up bro..and GG
    LOVE FROM INDIA

  • @jerrekedb
    @jerrekedb 6 ปีที่แล้ว +2

    I love how int(x^-x dx,x=0,x=1) = sum(j^-j,j=1,inf). Beautiful symmetry there

  • @asificare7985
    @asificare7985 3 ปีที่แล้ว +1

    I have no words to describe how beautiful the final result is. Also, this was one of your very well made videos :)

  • @drpeyam
    @drpeyam 6 ปีที่แล้ว +134

    Beautiful :)

    • @blackpenredpen
      @blackpenredpen 6 ปีที่แล้ว +15

      Dr. Peyam's Show hey!

    • @46pi26
      @46pi26 6 ปีที่แล้ว +6

      Three of my favorite mathematicians all in one spot! Yay!

    • @blackpenredpen
      @blackpenredpen 6 ปีที่แล้ว +4

      46 and pi yay!!!!!!

    • @wduandy
      @wduandy 6 ปีที่แล้ว +1

    • @johelgoni9438
      @johelgoni9438 5 ปีที่แล้ว

      Yee

  • @PalikkaFilms
    @PalikkaFilms 6 ปีที่แล้ว +56

    you lost me at infinity boi

  • @postnubilaphoebus96
    @postnubilaphoebus96 5 ปีที่แล้ว +6

    I don't understand a lot about maths but it seems like substitution is a very important technique for proofs. Also, it's handy to know similar functions so you can look at similarities.

  • @kevinchang1371
    @kevinchang1371 4 ปีที่แล้ว +3

    Dankest maths channel I have ever seen 🐸👌🏻🎩

  • @TuningFreak23
    @TuningFreak23 6 ปีที่แล้ว +43

    Its 1:30 AM I'm high and watching this. Dudeeee

  • @cliffordwilliams9597
    @cliffordwilliams9597 4 ปีที่แล้ว

    I barely understood what was going on and I LOVED IT! How did I just discover this channel? I love that the answer at the end was "like, 1.29something...?" Who cares about the answer when you have this beautiful process!

  • @nestorv7627
    @nestorv7627 6 ปีที่แล้ว +12

    please keep doing these beautiful integrals

  • @louismolywacky634
    @louismolywacky634 5 ปีที่แล้ว

    So beautiful solution with your rythmical good tempo as well as german like intonation and pronunciation. I love it.

  • @charlie3k
    @charlie3k 6 ปีที่แล้ว +49

    ah so you're an English major

    • @charlie3k
      @charlie3k 2 ปีที่แล้ว

      I’m just now coming back to this video 4 years later and now I fully understand it after taking calculus courses! I don’t even remember commenting on this video either.

  • @arthurgames9610
    @arthurgames9610 5 ปีที่แล้ว +1

    Waaaaai. X^-x=1/x^x. We can call it f(x). So, integral of f(x) at 0 to 1= 1/1^1 +1/2^2... but, this is exaticly f(1) + f(2)...
    Edit: im sorry if us duficult to understand this, its because im Braziliam, im not so good at English

  • @darthyoda4085
    @darthyoda4085 5 ปีที่แล้ว +3

    I think it's surprising that the integral from 0 to 1 of x^(-x) is exactly the sum from 1 to infinity of x^(-x)

  • @tay1545
    @tay1545 6 ปีที่แล้ว +4

    I just started learning calculus a few months ago, these videos are awesome because you do all the basic steps as well like at 1:13 , at my university the professors and teachers and even the university textbook never showed that step, it just showed 1:36 lol, great vids dude you make learning math seem just fine to a laymen.

  • @LaTortuePGM
    @LaTortuePGM 6 ปีที่แล้ว +4

    lol reminds me that time when i asked on >implying what was the sum from n=1 to infinity of 1/x^x and someone said it probably didn't have a closed form but that it was equal to this integral.

  • @_DD_15
    @_DD_15 6 ปีที่แล้ว

    We have the same way of reasoning and learning as far as I have seen. You don't make many analogies, I love your videos, keep going mate.

  • @seanlewis3867
    @seanlewis3867 3 ปีที่แล้ว

    It is very interesting the way your final result looks almost the exact same as your original problem, just in a discrete form

  • @ianprado1488
    @ianprado1488 6 ปีที่แล้ว +4

    There is some interesting semmetry between the initial problem and the solution

  • @przemysawrusin599
    @przemysawrusin599 6 ปีที่แล้ว

    You make me smile a little bit every time you say 'infinity boi' :) subscribed!

  • @alexandrokivistov8983
    @alexandrokivistov8983 5 ปีที่แล้ว

    Now this is my favorite video of your channel

  • @paulg444
    @paulg444 5 ปีที่แล้ว +1

    I like the way he pulled the -1^k /k! in from the cold !!

  • @kevinmartin7760
    @kevinmartin7760 6 ปีที่แล้ว +2

    I find it interesting that the integral from 0 to 1 of x^-x dx ends up being the sum from 1 to infinity of j^-j

  • @robertl.crawford4369
    @robertl.crawford4369 3 ปีที่แล้ว +1

    Nice job man, I really liked it and you!

  • @Ryan-gq2ji
    @Ryan-gq2ji 4 ปีที่แล้ว +2

    I started panicking when you wrote dx = -e^u du, but I calmed down when you subtly rewrote it as -e^-u du
    xd

  • @mokouf3
    @mokouf3 5 ปีที่แล้ว +2

    You can do one more step!
    It is equivalent to Sum(x=1 to ∞, x^(-x))
    The integrand of original integral is exactly same as the addend of the infinite summation!

    • @frenchimp
      @frenchimp 2 ปีที่แล้ว

      Yes, that's a mesmerizing result!

  • @gltchey
    @gltchey 6 ปีที่แล้ว +8

    integral from 0 to 1 of 1/x^x dx = sum from 1 to infinity 1/k^k
    cool

    • @sergiokorochinsky49
      @sergiokorochinsky49 6 ปีที่แล้ว +1

      ...I just can't see an intuitive geometric argument to explain why "0 to 1" became "1 to infinity".

    • @erenlapucet398
      @erenlapucet398 6 ปีที่แล้ว

      I wonder now if it's possible to find a function whose integral is finite and is exactly equal to its infinite sum with the same boundaries (obviously one of the boundaries being infinity)

  • @aniruddhvasishta8334
    @aniruddhvasishta8334 4 ปีที่แล้ว +1

    It's pretty neat that the integral from 0 to 1 of x^(-x) is just equal to the sum from 0 to infinity of x^(-x).

  • @regulus2033
    @regulus2033 5 ปีที่แล้ว +2

    Really interesting integral, thank you! The nice thing is that we integrate x^(-x) and get sum of k^(-k), very symmetric thing :)

  • @DiamondSane
    @DiamondSane 6 ปีที่แล้ว +4

    The more I see those integration puzzles the more I love numerical methods.

  • @benjaminbrat3922
    @benjaminbrat3922 6 ปีที่แล้ว +2

    So the integral of this function from 0 to 1 is just the infinite sum of the same function from 0 to infinity? There is something more to dig there.

  • @phyarth8082
    @phyarth8082 5 ปีที่แล้ว

    This function have optimization task answer is e^-e by away it second example where e=2,718 have minimum value property.

  • @simonsidorov8315
    @simonsidorov8315 6 ปีที่แล้ว +1

    It's an interesting result that the integral of x^{-x} is equal to the sum of the very same thing with x taking discrete positive values. At least it's the first time I see a function with a property like that

  • @APPLEZACKS
    @APPLEZACKS 6 ปีที่แล้ว +7

    Literally liked the video before I even started watching it

  • @wildatakalamingan2635
    @wildatakalamingan2635 6 ปีที่แล้ว +1

    First video to reach 100k+ views. proud of you :)

    • @Hawilabas
      @Hawilabas 4 ปีที่แล้ว

      It's me, I used my mom phone to watch and commented, now you already passed 100k subscribers, very proud of you papa flammy, time flies~

  • @revilo7389
    @revilo7389 6 ปีที่แล้ว +4

    Can you do a video explaining the interchange of the sum/integral and show some examples where it doesn't work? Or do a video on uniform convergence?

  • @shrimpchem
    @shrimpchem 5 ปีที่แล้ว +1

    So, you're telling me that the integral of a function is an infinite sum of infinitely small terms from that function. Sounds about right if you're looking to define what an integral is

  • @aczajka74
    @aczajka74 4 ปีที่แล้ว

    The integral that was massaged into a gamma function was also just the Laplace transform of u^k evaluated at k+1

  • @nitinsadras
    @nitinsadras 6 ปีที่แล้ว +28

    i n f i n i t y b o i

  • @testusernameyoutube1
    @testusernameyoutube1 5 ปีที่แล้ว +5

    Find someone who looks at you like our boi looks at the integral at 6:06

  • @VideoPerfection
    @VideoPerfection 6 ปีที่แล้ว +13

    what the fuck even is math

  • @adamtaylor1739
    @adamtaylor1739 6 ปีที่แล้ว

    How have I only just found this channel? It's awesome!

    • @adamtaylor1739
      @adamtaylor1739 6 ปีที่แล้ว

      Hey, can I ask what your 'day job' is?

  • @yourlonglostcousin
    @yourlonglostcousin 6 ปีที่แล้ว +1

    I don't understand why moving from du to -du helps fix the problem of the natural log going to negative infinity. Now the infinity is positive but why does that help?

    • @yourlonglostcousin
      @yourlonglostcousin 6 ปีที่แล้ว

      Couldn't you just leave it a positive du and make your lower bound for the next integral negative? That seems more natural to me

  • @skippycochrane1839
    @skippycochrane1839 6 ปีที่แล้ว +2

    i love the way you teach x) if my lecturer spoke like this i would be laughing none stop

  • @debajyotisg
    @debajyotisg 6 ปีที่แล้ว

    These videos make me so happy!

  • @CossZt6
    @CossZt6 6 ปีที่แล้ว

    That (-1) getting canceled out was one of the most satisfying things I've seen in some time lately

  • @Eymonn
    @Eymonn 6 ปีที่แล้ว

    To y'all wondering why you can interchange sum and integral, and if I'm wrong please correct me:
    The sum(fn) series converges uniformly on an interval L, aka , with fn(x) = (-1)^n * x^k * ln(x)^k * 1/k!
    -> sum (sup[x€L] |fn(x)|) converges
    This condition is enough for the infinite boi and the integral to be switched.

  • @Justin-dk9rl
    @Justin-dk9rl 6 ปีที่แล้ว +1

    Can you explain why the integral evaluated from 0 to infinity is so close to 2 but just a little less? Or why from 1 to infinity it's so close to 1/sqrt2? Maybe there is a nice explanation similar to the one with the Borwein integrals.

    • @Justin-dk9rl
      @Justin-dk9rl 6 ปีที่แล้ว

      Flammable Maths thanks for your quick response although i still don't believe it's a coincidence.
      Keep up the good work👍🏽

  • @amansatyarthi4110
    @amansatyarthi4110 4 ปีที่แล้ว +1

    i think without doing this any one can do it simply by taking y=(whole integration )
    and then take log on both side and then apply product rule

  • @mark_tilltill6664
    @mark_tilltill6664 4 ปีที่แล้ว

    Generalize inegral(a,b,f(x)) = integral (a,b, g(g-1(f(x))) g is a function with some properties

  • @ChrisLuigiTails
    @ChrisLuigiTails 6 ปีที่แล้ว +1

    Infinity boi
    Memes and maths. Subscribed.

  • @erwinrojasarabia
    @erwinrojasarabia 6 ปีที่แล้ว

    I saw your videos thinking I was subscribed lol, definitely your charisma makes me concentrate completely on the video haha

  • @thejusunnivelan7193
    @thejusunnivelan7193 6 ปีที่แล้ว

    The integral from 0 to 1 of a function is equal to the summation of that function from 1 to infinity, that function being x^-x

    • @omp199
      @omp199 6 ปีที่แล้ว

      Hmm. What other functions have the same property? We should name them "flammable functions", or something.

  • @kamrons8250
    @kamrons8250 6 ปีที่แล้ว +3

    Damn I miss calc. Saw this video on recommendation, very easy to follow and nicely explained.

  • @christophercampbell6906
    @christophercampbell6906 5 ปีที่แล้ว +1

    prob bois saw the reciprocal of the scaling factor for a gamma density right away

  • @HeavisideDelta
    @HeavisideDelta 5 ปีที่แล้ว

    Another approach : Instead of using the Gamma function you could have noticed that u^k.exp(-ku+1) ist - k th derivative with respect to k now using the Leibniz rule you can bring rhe derivative out evaluate the integral and then get a nice formula for your infinity boi

  • @gammafirion9162
    @gammafirion9162 6 ปีที่แล้ว +12

    Bro can u show us how to integrate x^( 1/x )

    • @sansamman4619
      @sansamman4619 6 ปีที่แล้ว +5

      GammaFirion, and from zero to infinity

    • @Grassmpl
      @Grassmpl 5 ปีที่แล้ว

      Hint: Let u=1/x

    • @gregoriousmaths266
      @gregoriousmaths266 4 ปีที่แล้ว

      Is this some meme I’m not getting?

  • @konstantinsotov6251
    @konstantinsotov6251 3 ปีที่แล้ว +1

    Lol, i thought you used j for your jmaginary unit

  • @pandas896
    @pandas896 5 ปีที่แล้ว +1

    I am happy , I was able to do this question in another way.

  • @sebastiansanfunas4674
    @sebastiansanfunas4674 6 ปีที่แล้ว

    Love this content and love your videos, thanks math boi

  • @ArthurvanH0udt
    @ArthurvanH0udt ปีที่แล้ว

    just stumbled into this (after 5 yrs). But isn't this "just" the reciprocal value of the Bernouilli integral?

  • @37metalgearsolid
    @37metalgearsolid 6 ปีที่แล้ว +1

    Quite neat result. I think that (pedantically) one needs to make a convergence analysis when using Taylor's theorem to write the exponent as an infinite series as there is a potential problem near x=0.
    Nice video.

  • @Lionel94Ismail
    @Lionel94Ismail 6 ปีที่แล้ว

    Two mistakes
    First, you just can't substitute ln0 as infinity in the integral limit Because it's undefined
    Second, you can't exchange integral limits without changing the sine of the integral

  • @michaldvorak8586
    @michaldvorak8586 6 ปีที่แล้ว

    If i apply the riemann limit definition for the integral, i end up with very simmilar expression: \lim_{n\to\infty} \sum_{k=1}^n k^{-k} \frac{k}{n} ...

  • @sorcererstone3303
    @sorcererstone3303 6 ปีที่แล้ว

    Another great example. I need to watch how to solve an integral from here everyday. That will make my day!

  • @babaganamuktar9518
    @babaganamuktar9518 3 ปีที่แล้ว

    I think the answer might be -2.
    Try integrating it without introducing the sum notation. It's pretty amazing.
    Thanks for uploading this video, looking forward for more.

  • @almanahulzilnicdesuceava5379
    @almanahulzilnicdesuceava5379 6 ปีที่แล้ว +29

    I showed this work to my lil sister and just laughted and said "what.s his favourite pokemon?" :))))

  • @ibrahimanaz2424
    @ibrahimanaz2424 4 ปีที่แล้ว +1

    There is a mistake ... between 6:50-7:00 ... e^(-uk).e^(-u)=e^(-uk-u)=e^[(-u)(k+1)]
    But in solution k-1 is written...

    • @ibrahimanaz2424
      @ibrahimanaz2424 4 ปีที่แล้ว +1

      Sorry...i dont realize that your plus is like minus 😁

    • @PapaFlammy69
      @PapaFlammy69  4 ปีที่แล้ว

      no problem:)

  • @jimnewton4534
    @jimnewton4534 5 ปีที่แล้ว

    nice development. Not very difficult, but you have to make the right magical substitutions. Congratulations.

  • @hoodedR
    @hoodedR 4 ปีที่แล้ว +1

    Why am i watching this again...I just saw it two days ago, and now this is the third time. Oh well. Hi Papa!

    • @PapaFlammy69
      @PapaFlammy69  4 ปีที่แล้ว

      Glad to see you back then Ranjan! xD

  • @andromedarobinson777
    @andromedarobinson777 6 ปีที่แล้ว

    I wonder which functions, f, could replace x^-x in the first integral and final sum so that the integral from 0 to 1 of f(x) with respect to x equals the sum from k=1 to infinity of f(k).

  • @daBAAAAM
    @daBAAAAM 6 ปีที่แล้ว +1

    6:00 sooo when you switched the limits of the integral, you just took the -1 of the e^-u and you didn't touch the signs of the other terms?

  • @ooffoo5130
    @ooffoo5130 4 ปีที่แล้ว +1

    I have no clue how to do calculus and I usually understand about 10% of what's going on but I love this guy's videos

  • @antonvanboxtel7790
    @antonvanboxtel7790 5 ปีที่แล้ว +2

    I just scrolled down to see the bottom blackboard. I am not a smart man.

  • @pastorofmuppets7654
    @pastorofmuppets7654 6 ปีที่แล้ว

    3:36 Can you please elaborate on this(How you chose a substitution that converges). I'm new to this and would appreciate if you can give some sources to read more.

  • @michael-gary-scott
    @michael-gary-scott 6 ปีที่แล้ว

    Honestly the title is why I'm here. Subbed.