Integral of infinite product of roots

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  • เผยแพร่เมื่อ 13 ธ.ค. 2024

ความคิดเห็น • 73

  • @undying384
    @undying384 3 หลายเดือนก่อน +41

    I just cheered when I realised what you were doing, math is so cool.

  • @sicsmaunravelled6786
    @sicsmaunravelled6786 2 หลายเดือนก่อน +3

    That looked like a devilishly difficult problem at first. Then you twirled your chalk and, as if by magic, everything fell into place. You are a consummate teacher, young man, and I salute you.

  • @peterfocko8321
    @peterfocko8321 8 ชั่วโมงที่ผ่านมา

    Man, you are best math teacher ever. I never stop learning from you. Regards from Slovakia.

  • @duckyoutube6318
    @duckyoutube6318 3 หลายเดือนก่อน +11

    0:50
    This man knows our intuitive thoughts. Thats how you know you have an amazing teacher.

  • @DTLRR
    @DTLRR 3 หลายเดือนก่อน +11

    Never Stop Learning!!
    That's so true ☺️

  • @Sigma.Infinity
    @Sigma.Infinity 3 หลายเดือนก่อน

    Beautiful, elegant solution. Nice! I thought this would be hard but once I saw the pattern, it all fell into place easily.

  • @duckyoutube6318
    @duckyoutube6318 3 หลายเดือนก่อน +2

    This was easier than i thought it would be.
    Once you spot the 1/x! The ball just starts rolling. Using e-2 is just so simple and nice. I love it.

    • @duckyoutube6318
      @duckyoutube6318 3 หลายเดือนก่อน

      Im sorry 1/k!
      You know what i mean.

    • @leif1075
      @leif1075 3 หลายเดือนก่อน

      ​@@duckyoutube6318i don't see how anyone would ever spot that though..

    • @duckyoutube6318
      @duckyoutube6318 3 หลายเดือนก่อน

      @@leif1075 It comes from practicing algebra.
      I dont like the radical sign. So i always try to write it as an exponent instead.
      Example: sqrt(2)=2^1/2 or cube root of 2 as 2^1/3 or the 4th root as 2^1/4 ect..
      Once you do that you will realize that you are multiplying exponents. In this case the exponents are fractions. And so you can multiply straight across.
      Example (((2)^1/2))1/3)1/4)
      And so the bottom of the fraction is just 2*3*4*5.....
      And since we didnt start at 0, we can subtract 2 from the factorial since we know that 0!=1 and 1!=1
      Just make sure you look at the problem carefully. Calculus is all about algebra such that if you dont know your axioms and theorems, its going to be hard to solve quickly.
      Try seeing numbers as something besides their obvious value.
      Example: 4=2^2 or 120=5!
      Try understanding things on the most basic level. Thats what the greats do. From Aristotle to Feynman. Try to make it simple through understanding not memorization.

    • @duckyoutube6318
      @duckyoutube6318 3 หลายเดือนก่อน

      Im not sure why my reply didnt go through. TH-cam must have flagged for spam.
      I see it because i converted the radicals to exponents. Then realized that the bottom of the fraction (exponent) had a pattern.
      (1/2)(1/3)(1/4)
      Which is just 1/x!
      And we didnt start at 1 so we had to subtract 2 because...
      0!=1
      1!=1
      Calculus is all about testing your understanding of algebraic axioms. Then, applying the theorems of calc.
      Hope this helps

  • @kragiharp
    @kragiharp 3 หลายเดือนก่อน +4

    This, I had in high school.
    Afterwards I had another 2 years of math.
    So, not yet, but slowly but surely you're getting to topics I have never heard of before and you are starting to loose me.
    Eventually I will have to stick to math again in order to follow. But it's fun. I just need a little time to keep up.
    Thank you so much for bringing long forgotten math back to memory.
    ❤️🙏

  • @eurocouto
    @eurocouto 3 หลายเดือนก่อน

    Magical!... that's cool!... this is a pure 'Mathemagics'... Great performance! Thanks!

  • @nanamacapagal8342
    @nanamacapagal8342 3 หลายเดือนก่อน +3

    ATTEMPT:
    The inside can be rewritten as x^1/2! * x^1/3! * x^1/4! * x^1/5 * ...
    which simplifies to x^(1/2! + 1/3! + 1/4! + 1/5! + ...)
    which again simplifies to x^(e-2).
    The integration is easy now!
    Int(x^(e-2) dx) = x^(e-1) * 1/(e-1) + C

  • @Noah-ot1sv
    @Noah-ot1sv 2 หลายเดือนก่อน

    Wow man I couldn’t stop smiling by the end of the video! This is my first video I’ve watched from you and I’m definitely going to binge watch your channel! It’s amazing the way you run through things it just blows my mind!

  • @dougaugustine4075
    @dougaugustine4075 3 หลายเดือนก่อน +1

    Well done!! I'm amazed, as usual.

  • @abdelmajid3409
    @abdelmajid3409 3 หลายเดือนก่อน +1

    Very beautiful!

  • @RealEverythingComputers
    @RealEverythingComputers 3 หลายเดือนก่อน

    Great video. Simply amazing explanation!

  • @restymendez399
    @restymendez399 2 วันที่ผ่านมา

    Very cool solution, without the 2nd or 3rd step, i can't solve it anymore, thanks.

  • @williamspostoronnim9845
    @williamspostoronnim9845 3 หลายเดือนก่อน +1

    Безукоризненно! Интересно! ! Блестяще!!!

  • @LITHICKROSHANMS-gw2lx
    @LITHICKROSHANMS-gw2lx 3 หลายเดือนก่อน

    Brilliant answer sir, I just amazed

  • @juanrobles9232
    @juanrobles9232 3 หลายเดือนก่อน

    I am extremely grateful that you uploaded this video for those who are educators and those who wish to learn mathematical concepts. You are amazing teacher. I wish I had teachers like you with great coherent voice and pace as well.

  • @positivenozy6065
    @positivenozy6065 3 หลายเดือนก่อน

    This is so nice! Thank you a lot for this video 👍

  • @RyanLewis-Johnson-wq6xs
    @RyanLewis-Johnson-wq6xs 3 หลายเดือนก่อน +1

    I love your equations.

  • @fahreyalcaisary588
    @fahreyalcaisary588 3 หลายเดือนก่อน +1

    this is soo beautiful!

  • @maxborn7400
    @maxborn7400 3 หลายเดือนก่อน +2

    did get a chuckle out of me when you wrote it down in a exponential series. I was wondering, "what does 1/2 + 1/2/3 + 1/2/3/4 + ..." converge too, and didn't think it's just factorial summation lol

  • @ebrafif
    @ebrafif 3 หลายเดือนก่อน

    You are so cool man! I like every video of you.

  • @brucelayman525
    @brucelayman525 3 หลายเดือนก่อน +1

    great job

  • @kornelviktor6985
    @kornelviktor6985 3 หลายเดือนก่อน +1

    Wow MIT question I like it. Although I've never solved any mit bee questions yet, just some qualifier ones😅. But Im still proud of myself since Im only in high school

  • @ivanhuertas5307
    @ivanhuertas5307 3 หลายเดือนก่อน

    You are a genious my brother

  • @Abby-hi4sf
    @Abby-hi4sf 3 หลายเดือนก่อน +4

    So neat!. I just gave up watching to many radicals. Wonderful to watch you simplify it !

  • @nedmerrill5705
    @nedmerrill5705 3 หลายเดือนก่อน +1

    Good stuff!

  • @vishwaspawaskar3619
    @vishwaspawaskar3619 3 หลายเดือนก่อน

    Nice solution

  • @matthieuf.5280
    @matthieuf.5280 2 หลายเดือนก่อน

    wow i love your videos i'm a new french maths-teacher and i love your energy

  • @tenminuteretreat807
    @tenminuteretreat807 2 หลายเดือนก่อน

    Very cool integral!

  • @helmuntparra7926
    @helmuntparra7926 3 หลายเดือนก่อน +1

    UNA INTEGRAL MUY BELLA

  • @wira2562
    @wira2562 3 หลายเดือนก่อน +1

    So challenging!🎉🎉🎉

  • @pojuantsalo3475
    @pojuantsalo3475 3 หลายเดือนก่อน +1

    This was cool. 🙂

  • @mudspud
    @mudspud 3 หลายเดือนก่อน +1

    Awesome!!!

  • @Grecks75
    @Grecks75 3 หลายเดือนก่อน

    At first I tried to do different ways of substitution, trying to arrive at a recursion or something nice, but it didn't play out well. Then I read what you wrote in the description of the video, and it suddenly became easy... 😃

  • @nothingbutmathproofs7150
    @nothingbutmathproofs7150 3 หลายเดือนก่อน +1

    Nice!

  • @maburwanemokoena7117
    @maburwanemokoena7117 3 หลายเดือนก่อน +1

    It’s exciting when you solve a math problem which I can also solve.

  • @guerreromendieta
    @guerreromendieta 3 หลายเดือนก่อน +2

    i came to a point that i started to watch the videos to watch him and not the math

  • @mnpatel5286
    @mnpatel5286 2 หลายเดือนก่อน

    @3:54 error detection
    @3:55 small correction, big meaning!!! 👍

  • @surendrakverma555
    @surendrakverma555 3 หลายเดือนก่อน

    Thanks Sir

  • @Quillslash
    @Quillslash 3 หลายเดือนก่อน +5

    haven't finished the video yet
    My guess is that you use the infinite sum of 1/n! = e, so the integrand would be x^(e-2)

    • @sanamite
      @sanamite 3 หลายเดือนก่อน +1

      I didn't watch it past the first image of the problem, it looked pretty obvious we were getting the factorial reciprocals infinite sum missing n=0 and n=1, so you just had to substract 1/0! + 1/1! = 2 from e and then the integral is textbook indeed

  • @rhc-weinkontore.k.7118
    @rhc-weinkontore.k.7118 2 หลายเดือนก่อน

    👍

  • @alohamark3025
    @alohamark3025 3 หลายเดือนก่อน +2

    They never taught me this at MIT. (I went to Bullwinkle's school).

  • @colina64
    @colina64 3 หลายเดือนก่อน

  • @kornelviktor6985
    @kornelviktor6985 3 หลายเดือนก่อน

    4:53 Mr.e😂😂😂

  • @hskstudies2412
    @hskstudies2412 3 หลายเดือนก่อน

    Happy teachers day 😊

  • @cicik57
    @cicik57 3 หลายเดือนก่อน +1

    oh it is cool, the sum ofr roots is sum 1/n! starting from 2, so it is e - 2.
    intergal of x^(1/(e-2)) = (1/(e-2)+1) x^(1/(e-2)+1)

  • @sclearDevelopment
    @sclearDevelopment 3 หลายเดือนก่อน +1

    Hello Mr.
    Can you make a video on all these important series one is expected to know? I figured out all the solution until I was stumped by the sum of the reciprocals of the factorials.
    Thanks 🙏

    • @ProactiveYellow
      @ProactiveYellow 3 หลายเดือนก่อน

      When you get to a series like that, especially with factorial denominators, it usually implies a Taylor (or MacLauren) expansion, which is generally of the form f(x)/0!+f'(x)/1!+f''(x)/2!+...+fⁿ(x)/n!+... To infinity, where fⁿ(x) is the n'th derivative of the function at point x. For particular "nice" functions, if you add up all infinite terms, you get a power series (infinite polynomial) that perfectly approximates the function itself in a region. Any time you see this kind of structure, it is useful to try and find the function f(x) which gives that particular expansion. In this case, e^x is its own derivative, so it is the "purest" expansion that doesn't require weird modification for each term, thus 1/0!+1/1!+1/2!...=1⁰/0!+1¹/1!+1²/2!+... Which is e¹ (e^x evaluated at 1)

    • @sclearDevelopment
      @sclearDevelopment 3 หลายเดือนก่อน

      @@ProactiveYellow I do know this. I'm just asking for a video on series constants that are commonly used

  • @DC-pm5bi
    @DC-pm5bi 3 หลายเดือนก่อน

    I wish you were my maths teacher in 12th

  • @Simpson17866
    @Simpson17866 3 หลายเดือนก่อน

    I just did this one in my head! I can't remember the last time I've been able to do that with one of these :D
    x^ (1/2 + 1/6 + 1/24 + 1/120 + ...) = x^(e-1)
    ∫ x^(e-2) dx = x^(e-1) / (e-1) + C

  • @lubiemuze6368
    @lubiemuze6368 3 หลายเดือนก่อน

    I was seeing from far away a factorial as soon as I saw a problem.

  • @YohannesGetu-o3x
    @YohannesGetu-o3x 3 หลายเดือนก่อน

    Can you please prove the Lambert's W function?

    • @adw1z
      @adw1z 3 หลายเดือนก่อน +4

      There’s nothing to prove about it? It exists and it works

    • @YohannesGetu-o3x
      @YohannesGetu-o3x 4 วันที่ผ่านมา

      ​@@adw1z So I can have a B function that can undo W and it works😅

  • @RahulGupta-lk3qw
    @RahulGupta-lk3qw 3 หลายเดือนก่อน

    Sir pls try solving of iit jee advanced mathematics section which is lot tougher than mit...

    • @PrimeNewtons
      @PrimeNewtons  3 หลายเดือนก่อน

      I would really love to but JEE questions are either too long or requires niche knowledge.

    • @RahulGupta-lk3qw
      @RahulGupta-lk3qw 3 หลายเดือนก่อน

      @@PrimeNewtons sir u can try jee mains only question ,this is average questions and not lengthy also ,and they have a lot of interesting questions...

  • @comdo777
    @comdo777 3 หลายเดือนก่อน +1

    asnwer=1dx isit

  • @arkodasgupta0412
    @arkodasgupta0412 3 หลายเดือนก่อน

    did it all alone, it was easy

  • @maxvangulik1988
    @maxvangulik1988 3 หลายเดือนก่อน

    I=int(prod[n=2,♾️](x^(1/n!)))dx
    I=int(x^sum[n=2,♾️](1/n!))dx
    I=int(x^(e-2))dx
    I=x^(e-1)/(e-1)+C

  • @RyanLewis-Johnson-wq6xs
    @RyanLewis-Johnson-wq6xs 3 หลายเดือนก่อน +4

    Integrate[Sqrt[xCbrt[xSurd[xSurd[x,4]……,5]]],x] I=(x^(e-1))/(e-1)+C final answer

    • @oniondeluxe9942
      @oniondeluxe9942 3 หลายเดือนก่อน +3

      It’s appalling, that after more than half a decade of having computers around us, there is still no good and standardized way to express and render mathematical formulae in native written text on the internet.

    • @adw1z
      @adw1z 3 หลายเดือนก่อน +2

      @@oniondeluxe9942yeah they really need to somehow add LaTeX formatting into TH-cam comments, maths is just another language in the end. All the math communities would benefit from it

    • @oniondeluxe9942
      @oniondeluxe9942 3 หลายเดือนก่อน +1

      @@adw1z perhaps. But LaTeX is a very programmer oriented interface. They should have been able to come up with something smoother by now. But, where there is no potential for advertising - no interest.

  • @Sigint123
    @Sigint123 3 หลายเดือนก่อน

    Nice!