Bernoulli's integral has a few tricky things going on

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Пікірлер: 19

  • @jackkalver4644
    @jackkalver464413 күн бұрын

    I have to admit, the sum is a good form as it converges very quickly.

  • @user-pf6jl6mu1n

    @user-pf6jl6mu1n

    11 күн бұрын

    Riemann agrees... 😂

  • @adandap
    @adandap14 күн бұрын

    Such a beautiful result. 😊 The same calculation for x^(-x) gives a very nice symmetric result of Sum[1/n^n] (n=1, 2... )

  • @owl3math

    @owl3math

    14 күн бұрын

    Yes this one is nice! :)

  • @iqtrainer
    @iqtrainer7 күн бұрын

    This one is called Sophomore's dream. Dr. PK evaluated this a few months ago

  • @owl3math

    @owl3math

    6 күн бұрын

    Oh nice. I didn’t know that name for it

  • @iqtrainer

    @iqtrainer

    6 күн бұрын

    @@owl3math You and Dr PK should collab on an integral. You two are two math youtubers posting challenging integrals I know

  • @owl3math

    @owl3math

    6 күн бұрын

    @@iqtrainer I like Dr PK!

  • @uselesscommon7761
    @uselesscommon776119 сағат бұрын

    Pi/4 moment

  • @panyachunnanonda6274
    @panyachunnanonda62749 күн бұрын

    Very nice; problem+ solution.

  • @owl3math

    @owl3math

    9 күн бұрын

    Hi Panya. And thanks! 🙏😀

  • @PaoloACostantino
    @PaoloACostantino12 күн бұрын

    by reiiterate integration by parts

  • @isavenewspapers8890
    @isavenewspapers889011 күн бұрын

    I got a notification for this video while writing the name "Bernoulli".

  • @owl3math

    @owl3math

    10 күн бұрын

    oooooh weird

  • @Reetdawn
    @Reetdawn6 күн бұрын

    SIMPLE ANSWER: X^X-1/X-1

  • @owl3math

    @owl3math

    6 күн бұрын

    is that supposed to be x+1? Power rule :)

  • @alvargd6771
    @alvargd677113 күн бұрын

    u can shift to -\sum_{n=1}^\infty\frac{(-1)^n}{n^n} to make it nicer

  • @felipefred1279
    @felipefred127913 күн бұрын

    I thought that you would use Laplace transform again hahaha

  • @owl3math

    @owl3math

    12 күн бұрын

    ha! I do like to use that quite a bit :)