ONE BALLER INTEGRAL: int(0, π/4) ln(1-tan(θ))/tan(θ)

Поділитися
Вставка
  • Опубліковано 25 лис 2024

КОМЕНТАРІ • 36

  • @tirterra1222
    @tirterra1222 Місяць тому +42

    Basic arithmetic is the final boss of maths, don't worry we all struggle. I feel your pain.

    • @Haxislive766
      @Haxislive766 Місяць тому +1

      Then accept pain and know pain those who don't know pain will never understand true peice

  • @unturnedd
    @unturnedd Місяць тому +17

    that 1/16 - 1/6 gave me nightmares, truly the hardest problem

  • @r4_in_space
    @r4_in_space Місяць тому +12

    When the pathetically weak side boss comes back as the invincible main boss at the end of the game:

  • @CM63_France
    @CM63_France Місяць тому +1

    Hi,
    I was just working about retrieving the first integral by Feinman technic, a couple of hours ago. The one which is equal to pi^2/6 . If you try to solve the Basel problem starting from 1/(1-x)=1+x+x^2+x^3+... , by intregrating, then dividing by x, then integrating again, you come across this integral.
    "ok, cool" : 0:17 , 3:01 , 5:11 , 5:53 ,
    "terribly sorry about that" : 1:56 , 6:06 , 8:56 .

  • @douglasstrother6584
    @douglasstrother6584 Місяць тому +1

    From your thumbnail, I'm ready for some R-rated Math!

  • @MrWael1970
    @MrWael1970 Місяць тому

    Very nice result. Thank you

  • @3manthing
    @3manthing Місяць тому +5

    'Basic' arithemetic, yet everyone struggles with it. They say "Poisson is kept in small bottles." in this case, a 'basic' bottle.🤷‍♂

  • @xanterrx9741
    @xanterrx9741 Місяць тому

    Great solution , thanks for work your hard work that you've done to make this video exist.

  • @mcalkis5771
    @mcalkis5771 Місяць тому +1

    I know those videos don't tend to do too well, but I'd love to see you do some more physics at some point.

  • @mcalkis5771
    @mcalkis5771 Місяць тому +1

    It's been months and I can't think of a clever LOTR reference that relates to this.

  • @tacticaltoaster9143
    @tacticaltoaster9143 Місяць тому +2

    I thought I was alone 10:09 , I CSNT do arithmetic. On my CALC AP exam, I started counting with my fingers on the no calculator portion that made me do arithmetic…

    • @maths_505
      @maths_505  Місяць тому

      I used to be so good at it back in high school. Now it's my greatest weakness.

  • @txikitofandango
    @txikitofandango Місяць тому +1

    "one baller integral" Finally, an integral for us one-ballers

  • @ayush10tharollno16
    @ayush10tharollno16 Місяць тому

    Runner up best math video

  • @Calcprof
    @Calcprof Місяць тому +1

    Arithmetic is hard. I just use Mathematica. However Euler was awesome at it, computing ζ(2n) up to (IIRC) n= 6 or 7 or so.

  • @tirterra1222
    @tirterra1222 Місяць тому +9

    also you made an error at the very end and wrote ln²(2)/8 insteand of minus ln²(2)/8

    • @maths_505
      @maths_505  Місяць тому +4

      Check again😂

    • @tirterra1222
      @tirterra1222 Місяць тому

      @@maths_505 am I missing something ? I = I1 - I2 and I2 = -5π²/96 + ln²(2)/8

    • @jkid1134
      @jkid1134 Місяць тому +1

      ​@tirterra1222 12:32

    • @tirterra1222
      @tirterra1222 Місяць тому +2

      @@jkid1134 looks like I clicked out of the video too fast. That's on me :/

  • @achrafsaadali7459
    @achrafsaadali7459 Місяць тому

    I got to admit that your approaches to compute integrals are pretty awesome on an academic level however I think if you brush up on and make note of theorems and axioms on when it is allowed to differentiate ,switch sum sign with improper integral sign because the way I learned ,they were crucial to start off calculating , and I am sorry if my critique wasn't instructive

    • @maths_505
      @maths_505  Місяць тому +1

      Convergence of the integral function will suffice. You can show that using various tests like dominated convergence, Dirichlet's convergence test etc. I've solved alot of integrals using Feynman's trick and you can find all of them in the playlist. In alot of those videos, you'll find me explaining why the switch up of operators is justified. However I do skip over that often because (depending on the integral) I find it so trivial to the point that I just want to get on with the actual solution.

  • @shieldmytears
    @shieldmytears Місяць тому

    Nice video ! Can you please do more multivariable integrals :p

  • @elinope4745
    @elinope4745 Місяць тому

    It feels like you're just leading me in circles...

  • @insouciantFox
    @insouciantFox Місяць тому

    ln(1-x)/x = 1/xΣxⁿ/n => Σ xⁿ/n²|x=1 => ζ(2)

    • @maths_505
      @maths_505  Місяць тому +1

      You forgot the -1 for the log series expansion

  • @sozeran
    @sozeran Місяць тому

    First, at last

  • @rajivb9493
    @rajivb9493 Місяць тому

    There willl be minus before (1/8) ln^2 (2) in final result..

    • @maths_505
      @maths_505  Місяць тому +1

      @@rajivb9493 exactly what I got

    • @aravindakannank.s.
      @aravindakannank.s. Місяць тому +1

      ​@@maths_505Bro u also got me for a second to type that on comment but some part of my brain told let's wait till the end and there we go
      U pulled a prank on us .😂

    • @maths_505
      @maths_505  Місяць тому

      @@aravindakannank.s. 😂😂😂