A stunning integral from the 2023 MIT Integration Bee semi finals

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  • เผยแพร่เมื่อ 25 ธ.ค. 2024

ความคิดเห็น • 37

  • @Notthatkindofdr
    @Notthatkindofdr ปีที่แล้ว +14

    Remarkable use of Euler's formula to simplify the integral! But it seems to me like it would be easier starting at 6:00 to just expand e^(i sin x) into real and imaginary parts. It is then easy to find the imaginary part of the product of the three factors, which is what the integral equals, because Re{z/i} = Im{z}.

  • @mohan153doshi
    @mohan153doshi ปีที่แล้ว +2

    Such a beautiful evaluation and solution development. It has been a while since I have seen such a beautiful and fascinating evaluation. Way to go 505, and btw, this integral must not have screamed SOS as it was being taken apart; it too must have been fascinated by the beautiful solution development and enjoyed it.

  • @MrWael1970
    @MrWael1970 ปีที่แล้ว +12

    Really you have an excellent skills to do this. But you forget to write + Constant of integration, because this is an indefinite integral. Thank you for this nice video.

  • @slavinojunepri7648
    @slavinojunepri7648 ปีที่แล้ว +2

    Such a clean and artisque solution!

  • @r2k314
    @r2k314 ปีที่แล้ว +1

    I'm not ashamed to say It doesn't get more fun than that!

  • @zunaidparker
    @zunaidparker ปีที่แล้ว +1

    Holy. Shit. That was insane!

  • @mohammadalkousa2856
    @mohammadalkousa2856 ปีที่แล้ว

    Great!
    Recently it was published a book about MIT integration bee, under the title " MIT Integration Bee, Solutions of Qualifying Tests from 2010 to 2023"
    You can simply find it!

    • @Babyshark-co8ks
      @Babyshark-co8ks 5 หลายเดือนก่อน

      This is not a qualifying exam

  • @gumkiller9734
    @gumkiller9734 ปีที่แล้ว +22

    Could this be done without complex numbers

  • @polyreza
    @polyreza ปีที่แล้ว +1

    Awesome 🎉🎉

  • @mohammadalkousa2856
    @mohammadalkousa2856 ปีที่แล้ว

    Thanks!

  • @nicogehren6566
    @nicogehren6566 ปีที่แล้ว +1

    very well done

  • @illumexhisoka6181
    @illumexhisoka6181 ปีที่แล้ว +1

    At first look I wouldn't have guessed that the answer is even elementary

  • @insouciantFox
    @insouciantFox ปีที่แล้ว +2

    When in doubt... Euler did it. Somehow.
    And if it's not Euler, it's Gauss.

  • @illumexhisoka6181
    @illumexhisoka6181 ปีที่แล้ว +3

    After your video on the gamma double prime at one it had me thinking
    Can there be a formula for the nth derivative of gamma at 1
    I have put some values in Wolfram and I noticed a two things
    1 it's alternating
    2 it have gamma constant^n and have zeta at deferent values
    It will be amazing if it have been derived

  • @minhnguyen1338
    @minhnguyen1338 ปีที่แล้ว +2

    is there anyway without using Euler formula

  • @giuseppemalaguti435
    @giuseppemalaguti435 ปีที่แล้ว

    Complimenti, anch'io avevo usato la Re..,poi mi sono perso..

  • @元兒醬
    @元兒醬 หลายเดือนก่อน

    ok, cool
    terribly sorry about that

  • @ves7y775
    @ves7y775 ปีที่แล้ว +1

    Yeeeet

  • @vitaliiyevtushenko8750
    @vitaliiyevtushenko8750 ปีที่แล้ว +1

    plus a constant

  • @meartin
    @meartin ปีที่แล้ว

    Bro are you study on phone this?

  • @MachinimaCommentary1
    @MachinimaCommentary1 ปีที่แล้ว +1

    Can you integrate e^(arcsin(e^(arccos(e^(arctan(1/(ln(x)))))))dx?

  • @DougOfTheAntarctic
    @DougOfTheAntarctic ปีที่แล้ว

    Distracting background talking.

  • @rohitashwaKundu91
    @rohitashwaKundu91 ปีที่แล้ว +1

    I'm really hurt by the fact that you forgot to write +C.
    Like there ain't any more worse way to hurt a integral lover!😢

    • @laincoubert9657
      @laincoubert9657 ปีที่แล้ว +1

      grow up

    • @rohitashwaKundu91
      @rohitashwaKundu91 ปีที่แล้ว +1

      @@laincoubert9657 Like really?!
      I should say the same to you. If you can't understand a joke, I've nothing to say!

    • @laincoubert9657
      @laincoubert9657 ปีที่แล้ว

      @@rohitashwaKundu91 woah man calm down you look really upset maybe you should grow up

    • @rohitashwaKundu91
      @rohitashwaKundu91 ปีที่แล้ว

      @@laincoubert9657 I am already calm, man. And I think you are right about growing up, but I don't think I want to grow up like "you" otherwise I won't be able to understand a simple joke!

    • @dqdv7105
      @dqdv7105 ปีที่แล้ว +1

      ​@@rohitashwaKundu91 yea it seems you are very calm