An integral trick whenever you have (f+f’)*e^x (Berkeley Math Tournament Integral Bee)

Поділитися
Вставка
  • Опубліковано 12 лис 2024

КОМЕНТАРІ • 80

  • @blackpenredpen
    @blackpenredpen  4 дні тому +18

    The hardest integral from 2022 BMT Integral Bee: ua-cam.com/video/SxNXrL-_tYA/v-deo.htmlsi=miEQpyVcUqYwOlQB
    Get your Ultimate Calc 2 Integral sweatshirt here: amzn.to/3Cx7YMQ

  • @dentonyoung4314
    @dentonyoung4314 4 дні тому +75

    Very nice solution. My calculus had bene getting a bit rusty after more than 30 years without using it, but seeing your videos over the past year has gotten my mind back in the groove.

  • @proximitygaming8253
    @proximitygaming8253 4 дні тому +232

    LOL IM IN THE VIDEO. I've never used a chalkboard before (so you can't read what I even wrote) and I was too nervous for my eyes to even perceive the e^x, so I just integrated the fraction on instinct and got it wrong.

    • @ChaineYTXF
      @ChaineYTXF 4 дні тому +29

      I just thought you had developped your own system to write math faster abd was almost in awe😅

    • @lambdaprog
      @lambdaprog 4 дні тому +15

      Pro Tip: Less gaming, more math.

    • @nykztv
      @nykztv 4 дні тому +39

      @@lambdaproggrow up 🐈

    • @adityaagarwal636
      @adityaagarwal636 4 дні тому +2

      I think you f'ed it up being under pressure. Otherwise it's an easy one😅

    • @ensiehsafary7633
      @ensiehsafary7633 4 дні тому

      You're the right one or the left one?

  • @ronbannon
    @ronbannon 4 дні тому +28

    Another great problem to share with my students. As I tell my students, most integrals are rigged in your favor, and this is an excellent example of a problem written to work nicely,

  • @bodesshorts8640
    @bodesshorts8640 4 дні тому +20

    Another great video from a great man

  •  4 дні тому +12

    Beautiful solution! Simple is beautiful!

  • @Samir-zb3xk
    @Samir-zb3xk 3 дні тому +5

    I pretended the e^x wasn't there and did partial fractions, (then multiplied it back) resulting in the sum of 2 integrals. Then I did IBP on the second one allowing the integrals to cancel. Pretty cool integral.

  • @morevrai
    @morevrai 2 дні тому

    wow I haven’t done calc in a while and this helped me touch up on my understanding, this integral worked out beautifully

  • @digitalogy2807
    @digitalogy2807 4 дні тому +7

    That was insanely easy atleast considering we were taught that property of (f + f') e^x

  • @rtx-vu3xn
    @rtx-vu3xn 2 дні тому

    Finally. U upload 😊😊. I also love math.

  • @scottleung9587
    @scottleung9587 3 дні тому +1

    Cool - congrats to the BMT winners!

  • @yousciencelab5307
    @yousciencelab5307 4 дні тому +2

    Just learned a valid lesson. Great work. ❤

  • @SandroZeta
    @SandroZeta 3 дні тому +2

    u= e^x/(x+1)²
    du = (x-1)e^x/(x+1)³ dx
    Integrate : 1 du = u + C
    R = e^x/(x+1)² + C 😴

  • @dalek1099
    @dalek1099 4 дні тому +2

    I looked for quotient rule and since that has a square at the bottom I multiplied by x+1 to get (x+1)^4. Then, I differentiated e^x/(x+1)^2.

  • @franklinazegha3430
    @franklinazegha3430 4 дні тому +1

    An interesting way to integrate functions with the exponential function ✨✨

  • @tgeofrey
    @tgeofrey 2 дні тому

    The reverse product rule is dope

  • @megazebra228
    @megazebra228 День тому

    👍interesting, thank you

  • @Silver-cu5up
    @Silver-cu5up 4 дні тому +12

    Thats a very hard to see reverse product rule!

  • @RandomGuy-jj5ce
    @RandomGuy-jj5ce 4 дні тому +1

    Interesting integral and a great video.

  • @Cray_Science
    @Cray_Science 23 години тому

    I had been trying since the video was published. I have just given up few minutes ago.

  • @super-df8zp
    @super-df8zp 3 дні тому +1

    where can i get the questions? i practiced some from your instagram and they were really good

  • @fernandoaj6128
    @fernandoaj6128 3 дні тому

    Admiro muito o seu trabalho blackpenredpen ❤

  • @hardlineamerican8495
    @hardlineamerican8495 16 годин тому

    Hey blackpenredpen, could you graph x^x for x

  • @Thatlockedrole
    @Thatlockedrole 8 годин тому

    Woah I did this problem right 🎉

  • @ChickenPowder
    @ChickenPowder 3 дні тому

    I didn't touch calculus for 2 years and I solved it within minutes during a psychology lecture🤣probably because I dare not to go for the complicated methods (partial frac) and accidentally found the pattern by looking at the DI table

  • @nura8578
    @nura8578 4 дні тому

    If you do the u-sub and do integration on parts on one of the integrals, the two integrals cancel out and leave the uv term

  • @MathematicsPro-v6v
    @MathematicsPro-v6v 4 дні тому

    great sir

  • @ouronlinetutor6995
    @ouronlinetutor6995 4 дні тому +1

    Good!

  • @depressedguy9467
    @depressedguy9467 4 дні тому

    this was easy quest like crying for e^(f(x)+f'(x)) type form

  • @deniseockey6204
    @deniseockey6204 4 дні тому +1

    where does he teach? I think it would be great to take some of his calculus classes. It would be challenging.

  • @cdkw2
    @cdkw2 4 дні тому +1

    saw this as a shift 2 pyq

  • @happy.5
    @happy.5 4 дні тому

    Is Berkeley math integration bee have their webpage like mit integration bee??

  • @VarunPatwal
    @VarunPatwal 4 дні тому

    I knew that it will use this identity, maybe I could've done it few months earlier from now 😅

  • @mohammedgamersc9572
    @mohammedgamersc9572 4 дні тому

    when I first saw e^x I knew I had to use f(x)e^x but I forgot to do +and -1 ; but even then my real weakness is addition subtraction multiplication, heck I forgot long division 💀

  • @aaravsharma-q4s
    @aaravsharma-q4s 3 дні тому

    Did this in head....mit bee is much more fun tbh

  • @efekaya09
    @efekaya09 4 дні тому +1

    can you solve x^6=(x+1)^6

    • @thatapollo7773
      @thatapollo7773 4 дні тому

      x=-0.5 is only solution in R

    • @robertpearce8394
      @robertpearce8394 4 дні тому

      ​@@thatapollo7773You just did someone's homework.

    • @AySz88
      @AySz88 4 дні тому +5

      ​@@robertpearce8394 Fortunately if it's homework, they have no work to show for credit

  • @priyanshu95.
    @priyanshu95. 3 дні тому

    ❤❤❤

  • @omrishir6835
    @omrishir6835 4 дні тому +7

    Really elegant solution, but how are you supposed to guess this? 😮

    • @blackpenredpen
      @blackpenredpen  4 дні тому +21

      Thank you. And I would say experience definitely helps. I don’t think I can do it either if it was my first time seeing an integral like this.

    • @o_s-24
      @o_s-24 4 дні тому +3

      Practice. Adding and subtracting numbers like that is quite common actually when solving integrals

    • @craig4320
      @craig4320 4 дні тому +1

      Often the problems are specially constructed so that a trick like this will work. If you try to integrate a function that you found somewhere it could be very hard.

  • @prajeshmanimaranixb4038
    @prajeshmanimaranixb4038 4 дні тому

    This is my school question 😂😂 i got it😅😅

  • @cdkw8254
    @cdkw8254 4 дні тому

    E

  • @6310-c5h
    @6310-c5h 2 дні тому

    красиво

  • @barnalibora8449
    @barnalibora8449 2 дні тому

    In India we learn this in class 12 lol

  • @anirudhpratapsinghchauhan
    @anirudhpratapsinghchauhan 4 дні тому

    Orz

  • @raiyanhasan2171
    @raiyanhasan2171 4 дні тому

    Which county are you from sir?

  • @sarthakmishra7159
    @sarthakmishra7159 4 дні тому +2

    Class 12th NCERT
    INTEGRALS CHAPTER 😊😊

  • @depressedguy9467
    @depressedguy9467 4 дні тому +1

    first

  • @sanmukhsingh8507
    @sanmukhsingh8507 4 дні тому

    Lol took 20 seconds.

    • @robertveith6383
      @robertveith6383 4 дні тому

      Laugh out loud. You're a liar. Shut up.

    • @Angelthathateshumans
      @Angelthathateshumans 4 дні тому

      ​@@robertveith6383 even a normal class 12 student can solve that in 20 seconds.

  • @darkfreeway
    @darkfreeway 4 дні тому +3

    What is the point of calculus when it’s impossible to always get it right and costly to get it wrong? Too many rabbit holes. How is it possible to usually get the calculus right when it’s impossible to never get the algebra wrong?