A brutal iterated integral!

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  • Опубліковано 6 лис 2024

КОМЕНТАРІ • 30

  • @CM63_France
    @CM63_France 6 місяців тому +16

    Hi,
    "ok, cool" : 0:10 , 6:20 , 7:24 , 9:11 , 10:41 , 11:54 , 16:31 , 16:51 , 19:52 ,
    "terribly sorry about that" : 4:48 , 9:51 , 11:37 , 19:14 .

  • @riadsouissi
    @riadsouissi 6 місяців тому +12

    Nice integral.
    I got 7/32*zeta(3) instead of 7/64*zeta(3) and wolfram confirms numerically what I got. So you must have an extra 1/2 somewhere.
    By the way, I used the fourier series of log(sin) and log(cos) from the very beginning without intermediary steps. Faster.

    • @devinjohnson6384
      @devinjohnson6384 6 місяців тому +2

      I checked with wolfram too and the use of 7/64*zeta(3) matches the answer to the integral. I don't think he's wrong.

  • @edmundwoolliams1240
    @edmundwoolliams1240 6 місяців тому +1

    I think this is the most beautiful result I've seen on your channel! 😊😊
    And Catalan is such a top G it survived that cancellation in the last step 😂

  • @MrWael1970
    @MrWael1970 6 місяців тому +1

    This is awesome. Thank you for featured effort.

  • @alielhajj7769
    @alielhajj7769 5 місяців тому

    sin(koi/2) is is zero when k i even but when k is odd it depends on the form of this odd number, if k=4n+1 it is 1, if k=4n+3 it is -1

  • @abdulalhazred6328
    @abdulalhazred6328 6 місяців тому +3

    16:35 (-1)^(k-1) is always identical to 1 , for odd k

  • @yoav613
    @yoav613 6 місяців тому

    Very nice video!!(and also very funny,log2 never hurts😂😂)

  • @UnknownGhost97
    @UnknownGhost97 6 місяців тому

    Answer is (pi^2)/16 * ln 2

  • @Mathematician6124
    @Mathematician6124 6 місяців тому +1

    Hey friend😊. I solved it. But yeah I had to look up one thing, that's the fourier transform of ln(sinx), I don't know fourier 😢. After that I did it on my own. It was a brilliant sum.

  • @mickodillon1480
    @mickodillon1480 6 місяців тому +2

    Thats a tough 1

  • @RICHARDMULOWAYI
    @RICHARDMULOWAYI 6 місяців тому +1

    What material do you use to make these videos, I mean ipad, tablet, applications? Thanks.

  • @iWilburnYou
    @iWilburnYou 6 місяців тому

    Keep up the great work 💪

  • @neg2sode
    @neg2sode 6 місяців тому

    Hi Maths 505, absolutely awesome integral presented in this video!! Here is a (first) request from me of sqrt(sin(x)) integrated through (0, pi/2). My classmates and I are confused by the elliptic integral approach and are curious if there is a simpler solution (using the tricks mentioned in your channel).

    • @maths_505
      @maths_505  6 місяців тому

      Google geometric form of beta function. Followed by reaction between beta and gamma functions. It'll get you the answer super quick.

    • @neg2sode
      @neg2sode 6 місяців тому

      @@maths_505 Worked it out!! Thank you!!! The answer is sqrt(2)/sqrt(π)*gamma(3/4)^2 isn't it -> beautiful numbers!

  • @ChfAkhbar
    @ChfAkhbar 6 місяців тому

    Hi Kamal , hope you doing good , you’re name Means perfection in Arabic , you’re content means a lot to me, that’s why I created this channel to Do maths videos …

  • @shivamdahake452
    @shivamdahake452 6 місяців тому +2

    Hey, I wish to learn more about calculus after I am done with my JEE advanced next month, I aim to start out with self study. Can you recommend me any sources of information to go ahead, books or websites or other videos perhaps ?
    I am good with the basics, so I have a strong foundation to build on.

    • @venkatamarutiramtarigoppul2078
      @venkatamarutiramtarigoppul2078 6 місяців тому

      Advance ke baad waise bhi karna padega bro engineering maths mein yein sab rehta hein.

    • @DKAIN_404
      @DKAIN_404 6 місяців тому +1

      Mai bhi multi variable calc shrur karuga advance ke bad​@@venkatamarutiramtarigoppul2078

    • @DKAIN_404
      @DKAIN_404 6 місяців тому

      Basics ke liye Dr. Terfor bazzett

  • @restymendez399
    @restymendez399 6 місяців тому

    it is possible to integrate it without limits because i doubt for the results, thanks.

  • @padraiggluck2980
    @padraiggluck2980 6 місяців тому

    I tried wolfram with the inner integral and just a constant for tan(y) and wolfram said, “No, thank you.”

  • @decendium
    @decendium 6 місяців тому

    i love you maths 505

  • @petterituovinem8412
    @petterituovinem8412 6 місяців тому +1

    that's a lot of stuff

  • @suryamgangwal8315
    @suryamgangwal8315 6 місяців тому +9

    Not the aprey's constant🫣

  • @toufikakkak8459
    @toufikakkak8459 6 місяців тому

    Nice

  • @suryamgangwal8315
    @suryamgangwal8315 6 місяців тому

    No audio

    • @maths_505
      @maths_505  6 місяців тому +6

      Good that's what I was going for.

    • @mickodillon1480
      @mickodillon1480 6 місяців тому +1

      @@maths_505 lol