A crazy approach to the gaussian integral using Feynman's technique

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  • Опубліковано 27 лис 2024

КОМЕНТАРІ • 86

  • @Decrupt
    @Decrupt Рік тому +180

    NOT THE REVERSE COWGIRL FOR INTEGRALS NOOOOO

    • @maths_505
      @maths_505  Рік тому +25

      😂😂😂

    • @stapler942
      @stapler942 Рік тому +45

      This is the first time in my life I have ever heard the phrase "reverse cowgirl" applied to mathematics and it's got me giggling. 😂
      Physics: "for simplicity in this example we will assume a spherical reverse cowgirl in a frictionless vacuum..."

    • @RichardJohnson_dydx
      @RichardJohnson_dydx Рік тому +4

      Unexpected but welcomed.

    • @TheArtOfBeingANerd
      @TheArtOfBeingANerd Рік тому +3

      No because I told my mom I would keep my youtube PG while watching my brothers and she literally walked in when it said reverse cowgirl

    • @jmcsquared18
      @jmcsquared18 5 місяців тому

      ""Physics is like sex. Sure, it may give practical results. But that's not why we do it."
      - Dick Feynman, who probably enjoyed cowgirl

  • @zahari20
    @zahari20 Рік тому +79

    In my opinion, the smoothest evaluation of the Gauss integral is to take its aquare, write it as a double integral, and use polar coordinates.

    • @TechToppers
      @TechToppers Рік тому +5

      Yeah I saw some paper and they said... This is an elementary approach so much more tricky to find. More advanced techniques make it way more trivial.

  • @zdzichumis
    @zdzichumis Рік тому +9

    What a truly beautiful way to evaluate the Gaussian integral! Your work shall not be underappreciated.

  • @madhurpopli1790
    @madhurpopli1790 4 місяці тому +1

    thanks a tonnn !!! i can finally understand this integral because the feynmann technique is fantastic. i can literally understand the gaussian integral at 17 !! THANKS A TONNN

  • @zunaidparker
    @zunaidparker Рік тому +5

    Another awesome integral! Can't stop watching these!

  • @_nemo171
    @_nemo171 Рік тому +6

    No fancy uses of Gamma function properties, a clean approach. Nice!

  • @BalajiKomanabelli-nd1xq
    @BalajiKomanabelli-nd1xq Рік тому +10

    At some point it looked like Laplace's approach but it is actually a great approach.
    But the easiest way is squaring and using polar coordinates

  • @cot2a
    @cot2a Рік тому +3

    Another way is, simply do substitution x^2 = t, then use Feynmann technique within this use the Gamma function and then the Laplace transformation porperty, L [f(t)/t] = int{s to inf} L(S) ds.

  • @christophermorris486
    @christophermorris486 Рік тому +28

    😂😂😂 I was hooked at reverse cowgirl trick for integration

    • @maths_505
      @maths_505  Рік тому +12

      If only youtube would allow me to use the corresponding thumbnail

    • @daddy_myers
      @daddy_myers Рік тому +3

      @@maths_505 Technically you could, you'd just have to use a different platform.

    • @maths_505
      @maths_505  Рік тому +16

      Ah yes....maths 505 on the hub😂

    • @christophermorris486
      @christophermorris486 Рік тому +1

      I did watch the video with on hand….the other hand was had a pencil in it following along

    • @maths_505
      @maths_505  Рік тому +7

      Had us in the first half not gonna lie

  • @trelosyiaellinika
    @trelosyiaellinika Місяць тому

    Cool! Really cool! I do not know how many ways to solve the Gaussian integral I have seen so far, including contour integration, and I am still fascinated and excited by yet another approach... Yes, maybe squaring and using polar coordinates is the easiest and most popular way but using various other approaches is a good massage for the brain... Besides, it keeps your vigilance to be able to see similar possibilities in solving other integrals.

  • @yoihenbalaishram8903
    @yoihenbalaishram8903 Рік тому +2

    That was very, very clever. Especially the substitution part....

  • @jmcsquared18
    @jmcsquared18 5 місяців тому +2

    "A crazy approach" That alone tells you that it's gonna work.

  • @pacotaco1246
    @pacotaco1246 Рік тому +1

    This is a really cool way to do it besides switching to polar. Nice!

  • @doroffixial
    @doroffixial Рік тому +2

    I couldnt even do simple equations in math yet i‘m here watching this and literally understanding zero. This stuff gives me ptsd from highschool times.

  • @cadmio9413
    @cadmio9413 5 місяців тому

    Thanks, this is one of my favourite videos on all the platform, never really understood polar cordinates :p

  • @cameronspalding9792
    @cameronspalding9792 Рік тому +2

    I would define the square of the integral to be J(t) not I(t), namely because I is defined as being the integral from zero to infinity.

  • @terrariariley1643
    @terrariariley1643 5 місяців тому +1

    I watched the video and started crying after 40 seconds

  • @circuitcraft2399
    @circuitcraft2399 Рік тому +6

    Doesn't 2:00 follow from the fundamental theorem of calculus, no differentiation under the integral required?

    • @maths_505
      @maths_505  Рік тому +4

      Indeed it does but the Leibniz rule provides a nice insight into its mechanism

    • @Singularitarian
      @Singularitarian Рік тому +1

      You’re right, we should just use the fundamental theorem of calculus at that step.

  • @mohamednour7680
    @mohamednour7680 Рік тому

    We can use the gamma function and it will be in the end gamm(1/2)= √π

  • @AndDiracisHisProphet
    @AndDiracisHisProphet Рік тому +1

    excellent thumbnail choice

  • @yudoball
    @yudoball Рік тому +1

    That's a cool trick

  • @Chris_387
    @Chris_387 Рік тому +1

    When taking the derivative why you do these with the limits? Is there a general rule?

    • @maths_505
      @maths_505  Рік тому

      The Leibniz rule

    • @Chris_387
      @Chris_387 Рік тому

      @@maths_505 okay and why d(0)=0?, how do you evaluate if you have a number

  • @aayushiajith.
    @aayushiajith. Рік тому +2

    Can anyone suggest me a book to start with feynmanns integrals???

    • @robertbachman9521
      @robertbachman9521 Рік тому +3

      Paul Nahin's 'Inside Interesting Integrals' is an entertaining book. He has a Chapter on Feynman's technique and another on contour integration. That is only 2 of the 9 chapters. There are some mind blowing problems in there about realistic problems from math and physics.

    • @indescribablecardinal6571
      @indescribablecardinal6571 11 місяців тому

      ​@@robertbachman9521Thank you very much, this will be so helpful for physics.

  • @chengfang545
    @chengfang545 7 місяців тому

    I didn't quite understand the change of variable in 3:31 can someone explain? thank u

  • @michaelbaum6796
    @michaelbaum6796 Рік тому

    Thanks a lot for this cool solution👌

  • @NightWanderer31415
    @NightWanderer31415 Рік тому +4

    Very nice! Nitpicking, you could have explained why the limit can be taken inside the integral in the final step.

    • @maths_505
      @maths_505  Рік тому +9

      Ah yes the interchange of limits....you're right....although the integral's convergence is trivial given its form it would've been better to mention this to justify taking the limit inside the integral operator

  • @aryaghahremani9304
    @aryaghahremani9304 10 місяців тому

    bro just pulled a reverse feynman technique, never seen a partial derivative be taken out of the integral
    wtf did I just watch lmao

    • @maths_505
      @maths_505  10 місяців тому

      The reverse cowgirl formulation of calculus

  • @pseudonimo224
    @pseudonimo224 2 місяці тому

    Awesome!!!!

  • @randomeme3484
    @randomeme3484 Рік тому +1

    Well gamma function is op

  • @Fr_Epic
    @Fr_Epic Рік тому

    What application is he using to solve this integral?

  • @andikusnadi1979
    @andikusnadi1979 Рік тому

    at 0:54 why its square ? thank you sir.

    • @maths_505
      @maths_505  Рік тому

      Watch the rest of the video
      It'll become clear

  • @chrissch.9254
    @chrissch.9254 Рік тому

    Lovely!

  • @mars_titan
    @mars_titan Рік тому

    How can I suggest you a problem? Mail?

    • @maths_505
      @maths_505  Рік тому

      It's in the about section of the page

  • @rythmx123
    @rythmx123 Рік тому

    how did u come up with the I(t) and then square it lol

    • @maths_505
      @maths_505  Рік тому

      I evaluated the fresnel integrals the same way so I applied it here. I got the fresnel integral approach from flammy but he messed up near the end with the complex exponential so I just improved on it.

    • @rythmx123
      @rythmx123 Рік тому

      @@maths_505 you're amazing man! no words only respect :)

    • @rythmx123
      @rythmx123 Рік тому

      @@maths_505 i'll be honest here, im just watching these vids for fun cuz my love's not with me and im kinda lonely and missing her haha... math's just awesome! i haven't studied calculus in that depth but watching you makes me realise there's so much i need to learn, thanks ❤️

  • @rido4822
    @rido4822 Рік тому +1

    U r Monster

  • @manstuckinabox3679
    @manstuckinabox3679 Рік тому +1

    ahh... a classic problem solved in a classic way, you should try with contour integration next.
    0:47 THIS IS NOT CLASSIC! THIS NOT CLASSIC AT ALL!

    • @maths_505
      @maths_505  Рік тому +1

      What else do you expect from the reverse cowgirl formulation of the gaussian integral 😂

    • @maths_505
      @maths_505  Рік тому

      You should check out qncubed3's video on the gaussian. It's pretty cool

    • @manstuckinabox3679
      @manstuckinabox3679 Рік тому

      @@maths_505 oh yeah I did, just wanted to see it from my fav youtuber, thought you might have a cool approach (his was also extrememly cool)

  • @worldnotworld
    @worldnotworld 23 дні тому

    I'm lost after 2:14...

  • @noobiegamer9080
    @noobiegamer9080 Рік тому +1

    Root pi

  • @yunwenzhu2193
    @yunwenzhu2193 Рік тому

    Seems to be overkill of this problem

  • @vatsalsharma4879
    @vatsalsharma4879 11 місяців тому

    I love maths

  • @sushil7276
    @sushil7276 Рік тому

    Why I am not smart like you

    • @maths_505
      @maths_505  Рік тому

      I'm not smart....just persistent...so you can do it if I can

  • @ahmeT0007
    @ahmeT0007 Рік тому +1

    Ramanujan solved like this by square root he used beta function

  • @Dodgevair
    @Dodgevair Рік тому

    Your thoughts on the current controlled extraterrestrial reality disclosure process and related US GOV cover-up?
    When the nervous contagious giggling subsides,
    how will our civilization adapt to this publicly known reality?
    What might be some of the potential implications of disclosure of this reality? New energy sources perhaps? Religions? History?
    Do we really want to know the full truth?

  • @georgesmelki1
    @georgesmelki1 Рік тому

    Why complicate things? It's useless! The polar coordinates method is still the best!

    • @maths_505
      @maths_505  Рік тому +1

      Gamma function approach is the simplest one....if anyone complains about the Γ(1/2) thing, I would direct them to the reflection formula for the gamma function.

    • @georgesmelki1
      @georgesmelki1 Рік тому +1

      @@maths_505 I agree. However, the polar coordinate approach is more elementary: we learned how to calculate the Gaussian before we evn heard about the gamma...