Solution 71: Forcing the u-Substitution to Work

  • Published on Dec 20, 2018
  • We modify the given expression such that a well-chosen u-sub instantly finishes the problem.
    Congratulations to Nicholas Patel, aby p, Parth Pawar, adandap, JiaMing Lim, Nitro Zox, Evyatar Baranga, Rishav Gupta, Peter, and Kostas Jelo for successfully solving the last week's math challenge question! Nicholas Patel was the first person to solve the question.
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Comments • 43

  • Luc De Graaf
    Luc De Graaf 19 days ago

    Hey man, I love this vid, but I don't understand why you need to set the exponent of the derivative of x^2n equal to 2018-n

  • spar
    spar 4 months ago

    Isnt it +-sqrt(8)?

    • santhanam krishnan bhaskar
      santhanam krishnan bhaskar 2 months ago

      Explanation for that given at the beginning of the video. Anyways I will say it again. Since when k increases the integrand increases, the maximum value of k will occur at the maximum value of the integrand, which being equal to +8 is larger than when being equal to -8.

  • Aditya Kondamudi
    Aditya Kondamudi 4 months ago +1

    Great solve!!!!!

  • Vaidhyanathan A
    Vaidhyanathan A 5 months ago +1

    What a beautiful problem,and how simple logics are used too,great,thank you sir..

  • Rishi Sarkar
    Rishi Sarkar 6 months ago

    this guy is a mad genius

  • Meh !
    Meh ! 8 months ago +8

    Interesting stuff!
    Your accent sounds little bit like blackpenredpen XD

  • Michael Empeigne
    Michael Empeigne 8 months ago +1

    Prove this following : if the bases are in arithmetic progression, and the exponent, n, is odd; then the expression is divisible by the sum of the bases.

    Written mathematically:

    [ a^n + ( a + d )^n + ( a + 2d)^n + ........ + ( a + ( r - 1 )*d )^n ] is divisible by r* [ 2a + ( r - 1 )*d ] / 2.

  • The unmastered
    The unmastered 8 months ago

    Can you upload more tricky u sub

  • The unmastered
    The unmastered 8 months ago

    I love this so much

  • magnifecent
    magnifecent 8 months ago +2

    can you try math olympiad?

  • Jonathan Liu
    Jonathan Liu 8 months ago +1

    Wasn't the problem originally asking for "all possible values of k?"

    • magnifecent
      magnifecent 8 months ago

      It was, however he meant it to say "largest value of k"

  • Jonathan Liu
    Jonathan Liu 8 months ago


  • Easy Mathematics
    Easy Mathematics 8 months ago +6

    Very tricky and nice solution.
    I guess this should be the most elegant solution. Beautiful. :)

  • petre Tepner
    petre Tepner 8 months ago +3

    Do you remember to put your socks on before your shoes?

  • Nicholas Leclerc
    Nicholas Leclerc 8 months ago

    "Nicholas Patel", huh, an "h" like me... you copycat ! (; p)

  • Andrés Robles
    Andrés Robles 8 months ago +1

    K no puede ser negativo también?

  • Just Weird
    Just Weird 8 months ago +1

    I tried both methods of Usub. Then thought I can try to make it its derivative and use that...though didn't know how. Thanks

  • δτ
    δτ 8 months ago

    Why is 2034 the largest possible value of k?

    • δτ
      δτ 8 months ago +2

      @Jia Ming
      Ah, ok.

    • Jia Ming
      Jia Ming 8 months ago +4

      The integral evaluates to -sqrt(8) for another value of k. That value is approx -6091.9754

    • δτ
      δτ 8 months ago +1

      Right, the function is given, so this manipulation gives the solution.
      My question was dumb.
      Thanks, anyway.
      But should 2034 then not be also the only solution?

    • Minh Cong Nguyen
      Minh Cong Nguyen 8 months ago +1

      if k>2034 then AUC of the curve is bigger than sqrt(8) (because the function is strictly increasing in respect of k). So 2034 is the largest possible value of k

  • Taufiqurrahman Datau
    Taufiqurrahman Datau 8 months ago

    What Is The App he use ?

  • Jeff Ahn
    Jeff Ahn 8 months ago +2

    Just wtf man

  • Rot
    Rot 8 months ago +3

    Mind blown

  • Parth Pawar
    Parth Pawar 8 months ago +1

    Amazing! Hey but what about that work done by spring analogy somebody did in the comments, I would like to know more about that!

  • Jon Snow
    Jon Snow 8 months ago +37

    you are the most craziest person on the youtube...

  • Ben Burdick
    Ben Burdick 8 months ago +4

    Well, I'm proud I at least tried this one. It was quite interesting; I would love a problem similar to this in the future.

  • Zyloh SZN
    Zyloh SZN 8 months ago


    PRAKHAR AGARWAL 8 months ago +4

    Great question with a mind blowing explanations!!!
    Never thought a solution could be made by forcing it and that it could be approached this way...
    Thanks Sir!!

  • زين العابدين ماجد

    Thanks you

  • Smokie Bear 🔴🔵
    Smokie Bear 🔴🔵 8 months ago +3

    I knew my explanation was pretty close.

  • Duran Chen
    Duran Chen 8 months ago


  • Joshua Cohen
    Joshua Cohen 8 months ago +2