1Psi3Colour
1Psi3Colour
  • 95
  • 155 670
An ABSURD Looking Integral With A NICE Result
It's been a while since I have done an integral video, so enjoy :)
Math Stack Exchange Post:
math.stackexchange.com/questions/520657/a-conjectured-closed-form-of-int-limits-0-infty-fracx-1-sqrt2x-1-ln-l
🔥Subscribe to 1Psi3Colour:
czcams.com/users/1Psi3Colour?sub_confrimation=1
👉Check out these playlists:
Math Olympiad Problems from Different Countries:
czcams.com/play/PLfdSlpebuC3Y2w4Pw2ftY1YAB6eYb0HVh.html
Math Shorts: czcams.com/play/PLfdSlpebuC3ZdBZZlnGj1G0yPeY0KSa1h.html
Functional Equations:
czcams.com/play/PLfdSlpebuC3a2WmfoW9J-IgTQry0a4XuE.html
👉Suggest a problem: forms.gle/hTibrUKz7QNyqoC48
zhlédnutí: 481

Video

THIS Indonesian Inequality Is JUST TOO GOOD To Be True!
zhlédnutí 223Před rokem
The Most Crazy-Looking Mathematical Inequality I have proved so far, it's so pleasing and elegant to have it proven. So, I have the whole proof presented to you in this video! It's from the 2011 Indonesia Mathematical Olympiad and it's insane to come up with such inequality! 🔥Subscribe to 1Psi3Colour: czcams.com/users/1Psi3Colour?sub_confrimation=1 💥Check out these videos: Can You Find The TWO ...
A Property Banned By Factorials.
zhlédnutí 782Před rokem
Enter the forbidden city of factorials where there are certain properties banned by factorials. Beware of everything you do, see and think. But to survive in this forbidden city, you must prove that the sum of first n factorials is never a perfect power. Remember! Beware of the proof! Typo at 3:51 and 0:23 : It should be " ... n!". 🔥Subscribe to 1Psi3Colour: czcams.com/users/1Psi3Colour?sub_con...
Solving a HARD Number Theory problem from the USA Math Olympiad Program
zhlédnutí 1,1KPřed rokem
Gear Up! We are going to solve a hard number theory problem from the 2004 USA Math Olympiad Program and... Don't just guess the solutions! Prove it! Let's see if you are capable of making into the math camp! Make sure to watch all of the video or else these triples (x, y, z) will come and find you at night. Typo at 0:23: A " " is missing. 🔥Subscribe to 1Psi3Colour: czcams.com/users/1Psi3Colour?...
This is NOT an ordinary triangle… | 1959 IMO Problem 4
zhlédnutí 376Před rokem
Say Hi to this unordinary triangle from the 1959 IMO! He is a right triangle with its median drawn to the hypotenuse is the geometric mean of his two legs... Well, make sure to watch all of this video to know how to construct him, or else he will be sad that you don't care about him... 🔥Subscribe to 1Psi3Colour: czcams.com/users/1Psi3Colour?sub_confrimation=1 💥Check out these videos: Can you so...
Can you solve this integral WITHOUT Feynman’s Method?
zhlédnutí 314Před rokem
Hey, I know you! You're the easiest integral I have ever done using Feynman's Method of Integration! Hmmm, yeah but we'll do it with double integrals this time! You better watch all of this video or else, you'll be dead if Feynman isn't available. 🔥Subscribe to 1Psi3Colour: czcams.com/users/1Psi3Colour?sub_confrimation=1 💥Check out these videos: 2010 IMO Shortlist Geometry: Let's Kill This!: cz...
How To Solve 2010 IMO Shortlist G1
zhlédnutí 244Před rokem
Wanna solve an IMO Shortlist Geometry Problem? Here's a cool one for you to solve! It's from 2010 IMO Shortlist Geometry, in order to kill this problem real quick, make sure to watch all of the video or else you will be killed by the problem.. But what is a Directed Angle? czcams.com/video/c4fdjmjRJ-c/video.html 🔥Subscribe to 1Psi3Colour: czcams.com/users/1Psi3Colour?sub_confrimation=1 💥Check o...
This Mysterious Sum CAN NEVER GO BEYOND 1
zhlédnutí 291Před rokem
What if I tell you that you have a chance at solving an inequality problem from the 2022 Malaysian IMO Training Camp? Well, here's a mathematical inequality for you to prove. Watch until the end of the video for a detailed explanation of the proof. Corrections (Typo): 1:09 The correct expression in the numerator of the summand should be x(√((x y)(x z))-x) instead of having all terms under the s...
Feynman’s Technique Is The MOST Overpowered Integration Technique EVER Existed!
zhlédnutí 981Před rokem
Do you know what is the MOST Overpowered Integration Technique? Of course, it is the Feynman's Technique Of Integration! And we are going to slay an integral which is hard to evaluate using standard techniques of integration using this trick! Watch until the end of the video and Feynman would be proud of you. 🔥Subscribe to 1Psi3Colour: czcams.com/users/1Psi3Colour?sub_confrimation=1 💥Check out ...
A Cool Inequality Proved With A Trick!
zhlédnutí 185Před rokem
A Cool Inequality Proved With A Trick!
You Won't Believe The Answer To This Limit
zhlédnutí 278Před rokem
You Won't Believe The Answer To This Limit
What Is the Proizvolov's Identity and How You Can Prove It!
zhlédnutí 600Před rokem
What Is the Proizvolov's Identity and How You Can Prove It!
How Oxford University Tests Math Applicants And How You Can Get In!
zhlédnutí 276Před rokem
How Oxford University Tests Math Applicants And How You Can Get In!
These Two (Directed) Angles Are The Same!
zhlédnutí 323Před rokem
These Two (Directed) Angles Are The Same!
15 Minutes to Solve the First IMO 1959 Day 1 -- Can YOU?
zhlédnutí 171Před rokem
15 Minutes to Solve the First IMO 1959 Day 1 Can YOU?
Coffin Problems: Primes vs Functions, Who Would Win?
zhlédnutí 687Před rokem
Coffin Problems: Primes vs Functions, Who Would Win?
Unlock the Secrets of Incenter and Excenter with this Geometry Lemma
zhlédnutí 241Před rokem
Unlock the Secrets of Incenter and Excenter with this Geometry Lemma
One of The "Easiest" IIT Math Problem I Have Ever Solved!
zhlédnutí 307Před rokem
One of The "Easiest" IIT Math Problem I Have Ever Solved!
Kyrgyzstan Mathematical Olympiad 2012 | Two Ways to Solve This Functional Equation!
zhlédnutí 522Před rokem
Kyrgyzstan Mathematical Olympiad 2012 | Two Ways to Solve This Functional Equation!
How Goldbach and Euclid Proved There Are Infinitely Many Primes?
zhlédnutí 1,4KPřed rokem
How Goldbach and Euclid Proved There Are Infinitely Many Primes?
British Maths Olympiad 2015: Can You Find The 2015th Term?
zhlédnutí 289Před rokem
British Maths Olympiad 2015: Can You Find The 2015th Term?
What is the Jensen's Functional Equation?
zhlédnutí 917Před rokem
What is the Jensen's Functional Equation?
What Are x and y?
zhlédnutí 201Před rokem
What Are x and y?
Coffin Problem: A Killer Sum from Soviet Union
zhlédnutí 468Před rokem
Coffin Problem: A Killer Sum from Soviet Union
Can you prove this CRAZY easy inequality?!
zhlédnutí 198Před rokem
Can you prove this CRAZY easy inequality?!
When is this a perfect square?
zhlédnutí 722Před rokem
When is this a perfect square?
Romanian Math Olympiad is Really Wild
zhlédnutí 998Před rokem
Romanian Math Olympiad is Really Wild
Can you find all "Norwegian" functions?
zhlédnutí 334Před rokem
Can you find all "Norwegian" functions?
The easiest problem on IMO training camp
zhlédnutí 848Před rokem
The easiest problem on IMO training camp
This Equation Changed Functional Equations Forever
zhlédnutí 2,5KPřed rokem
This Equation Changed Functional Equations Forever

Komentáře

  • @danieldandi2896
    @danieldandi2896 Před 2 dny

    In 7:20 why DAC=-CBD how you determine the - minus how to determine the clock or anticlockwise

  • @bladeiron
    @bladeiron Před 17 dny

    As someone in the American education system, I can confirm this was not part of our 12th grade math textbooks.

  • @Science_sachet_9710
    @Science_sachet_9710 Před 18 dny

    Answer is -69

  • @UdssRAP
    @UdssRAP Před 20 dny

    You still have to show that there are a,b,c‘s to attain the 81. You can use that equality in the Cauchy Schwarz inequality holds if the vectors are linear depending and for example a=1, b=3, c=5 should work.

  • @sakinsadaf4068
    @sakinsadaf4068 Před měsícem

    Can you please make a video on power of point?

  • @sakinsadaf4068
    @sakinsadaf4068 Před měsícem

    Thanks a lot!! Your video made me understand my first IMO problem’s solution.

  • @shalazoo8806
    @shalazoo8806 Před měsícem

    My ass did u= e^x+1, partial Fractions, and then evaluated ln(infinity) to get the same answer 💀💀

  • @Frrrkkkk
    @Frrrkkkk Před měsícem

    Erm what the Sigma

  • @yashwardhansingh220
    @yashwardhansingh220 Před měsícem

    Can also multiply by e^x both numerator and denominator and then take e^x = t

  • @ayushgautam2007
    @ayushgautam2007 Před měsícem

    12 class chindi questions

  • @shloksharma2839
    @shloksharma2839 Před měsícem

    Easiest question fr

  • @brainsmasher8288
    @brainsmasher8288 Před měsícem

    Easy 😂

  • @CalculusSlayer
    @CalculusSlayer Před měsícem

    i don’t get it

  • @speakingsarcasm9014
    @speakingsarcasm9014 Před 2 měsíci

    ok but how do you make sure that this is the only solution and there are no other?

  • @santiagososavasquez8529
    @santiagososavasquez8529 Před 2 měsíci

    Elegant solution 🎉

  • @keerthanas4144
    @keerthanas4144 Před 2 měsíci

    Ahh yes our textbook question for 12th grade.

    • @lonekoq4646
      @lonekoq4646 Před 22 dny

      as a 4th grader, this is very easy

    • @therealtdp
      @therealtdp Před 6 dny

      It's the qualifiers, this is made to boost your self confidence. Try some semi/finals questions

    • @keerthanas4144
      @keerthanas4144 Před 6 dny

      @@therealtdp ohhhhhh ohkayyyyy

  • @syedzain1776
    @syedzain1776 Před 2 měsíci

    The fact that you did the integration of lnx wrong

  • @TINTIN-91104
    @TINTIN-91104 Před 2 měsíci

    Shouldn't it be 1/12 instead of 1/6 🧐 ?

  • @gmncnr
    @gmncnr Před 3 měsíci

    Nice

  • @IbJr-nb2ff
    @IbJr-nb2ff Před 3 měsíci

    Cant we solve it using XBCY trapeze ?

  • @nehadjafary4456
    @nehadjafary4456 Před 4 měsíci

    How is xdx=ydy

    • @andunyaa
      @andunyaa Před 3 měsíci

      by cross product

    • @wmazim910
      @wmazim910 Před 8 dny

      ​@@andunyaa how => y^2/2 + C1 = x^2/2 + C2 ✅ => y^2 + 2C1 = x^2 + 2C2 ✅ => y^2 = x^2 + C ???? ⁉

  • @dipankarbanerjee1130
    @dipankarbanerjee1130 Před 4 měsíci

    We did it in 12th ! One of the easiest questions 😂😂

  • @samueldeandrade8535
    @samueldeandrade8535 Před 4 měsíci

    I guess I just found the most underrated math channel ever.

  • @user-lu6yg3vk9z
    @user-lu6yg3vk9z Před 5 měsíci

    I think it’s 1/12 not 1/6 square root 2

  • @imeprezime1285
    @imeprezime1285 Před 5 měsíci

    LoL, the title😂

  • @user-wu2vq9ew3i
    @user-wu2vq9ew3i Před 5 měsíci

    ✅个哦哦的个✅

  • @KylerHosek
    @KylerHosek Před 6 měsíci

    I just added e^x - e^x in the numerator and split it up

    • @dipankarbanerjee1130
      @dipankarbanerjee1130 Před 4 měsíci

      But it got lengthy! When solving integration one should be caring about time optimisation

    • @lonekoq4646
      @lonekoq4646 Před 22 dny

      ​@@dipankarbanerjee1130you prob did it wrong, I did it in a very optimized manner and took me basically 2 lines to solve it

    • @dipankarbanerjee1130
      @dipankarbanerjee1130 Před 22 dny

      @@lonekoq4646 no.. I was actually telling him.. I too did the problem in a short way

  • @samirait-kaci-gf3bn
    @samirait-kaci-gf3bn Před 6 měsíci

    How tf does that prove anything

    • @muhshaimebandomia649
      @muhshaimebandomia649 Před 5 měsíci

      😂😂😂😂😂

    • @imagod4796
      @imagod4796 Před 3 měsíci

      (f as the original expression and g as the formula you’re trying to prove) If we can show that f of any n of the natural numbers is equal to g of that same number then we can start our proof (im going to assume that this value is 0 to explain how the proof works later). We can now assume that f(n_0)=g(n_0). If we can show that f(n_0+1) = g(n_0 + 1) using the fact that f(n_0)=g(n_0), then it must be true for all n_0 greater or equal to n from the start. This is because we just showed the formula also works with 1 (because we know that f(0)=g(0) and that the same applies for that value (in this case 0) plus 1). We can repeat this same process using 1 instead of 0 to show that it works for 2 and so on to infinity.

    • @freshacado4304
      @freshacado4304 Před měsícem

      @@imagod4796..in English.. please? 🙏

  • @justsomeguy4933
    @justsomeguy4933 Před 6 měsíci

    I went from x ➡ -x world Same tho

  • @AliRaza-dz9gf
    @AliRaza-dz9gf Před 7 měsíci

    This is 12th board level question.

  • @hydronium_the_mysogynist
    @hydronium_the_mysogynist Před 7 měsíci

    We literally have it in our book

  • @NaN_000
    @NaN_000 Před 7 měsíci

    Nice problem

  • @simonmygind4504
    @simonmygind4504 Před 7 měsíci

    Solved it a bit different by use of sine and cosine. Got the same thing tho. Nice problem 😊

  • @user-qc9cd5iz3l
    @user-qc9cd5iz3l Před 7 měsíci

    We can also prove this by the formula of sum of 'n' numbers given by Carl Friedrich Gauss when he was just 10 years old. Let the Arithmetic progression be 1, 2, 3, 4, 5, 6, 7 ,8,...n Here, the first term=1=a Common difference=1=d Number of terms= n =n Using Gauss's formula for calculating sum of terms in an arithmetic progression, Sum of n terms= n/2[2a+(n-1)d] Substituting values we get, Sum of n terms=n/2[2(1)+(n-1)(1)] Sum of n terms=n/2(2+n-1) Sum of n terms =n/2(n+1) Sum of n terms =[n(n+1)]/2

    • @user-qc9cd5iz3l
      @user-qc9cd5iz3l Před 6 měsíci

      I just stumbled upon this video again

    • @masterjif9506
      @masterjif9506 Před 4 měsíci

      @@user-qc9cd5iz3lI just stumbled upon you stumbling on this video again

  • @oKanekei
    @oKanekei Před 7 měsíci

    this is literally just the dirichlet eta function evaluated at one

  • @nikshayyadav9472
    @nikshayyadav9472 Před 8 měsíci

    We do this in 12th grade.

    • @leo32190
      @leo32190 Před 6 měsíci

      That’s why it’s a qualifying question dude

  • @DatTrumpetBoi888
    @DatTrumpetBoi888 Před 8 měsíci

    Is it bigger than 10 {100} 10?

  • @s1mpelness771
    @s1mpelness771 Před 8 měsíci

    Cauchy schwarz inequality : (Ai^2)(Bi^2)>= (AiBi)^2

  • @Noam_.Menashe
    @Noam_.Menashe Před 9 měsíci

    I thought of the second way but for some reason I thought u to negative u doesn't cancel out...

  • @edupath2824
    @edupath2824 Před 9 měsíci

    ye to hamare yaha boards mein aata hai😂

    • @Ferrarifan537
      @Ferrarifan537 Před 9 měsíci

      Sahi kaha aapne 😅😅😂😂

    • @sukeshkamar6371
      @sukeshkamar6371 Před 9 měsíci

      Aapne khudke jan ko jokhim pe dalte hue bhi inti badi sach ko sabke samne lane ke liye naman hai aapko sir ..😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂

    • @subhradeepghosh8263
      @subhradeepghosh8263 Před 4 měsíci

      Ya Indian student solve ultra difficult questions just to get into a college and then majority ends up being an IT slave. US students on the other hand solve a way easier test, gets into colleges way better than any indian college and goes on to become scientists, engineers working on the forefront of technology..

    • @ommpradhan2799
      @ommpradhan2799 Před 3 měsíci

      ​@@subhradeepghosh8263its just a qualifier question . if you think MIT asks easy questions then solve the questions came in integration bee final 2024 .

  • @TsukkiSenpai727
    @TsukkiSenpai727 Před 9 měsíci

    How do we know left side is even?

  • @sumitvishwakarma1075
    @sumitvishwakarma1075 Před 9 měsíci

    whatttt this is a qualifier question ? Bro it is just Basic question for IIT JEE student

    • @HELLOHELLOISANYBODYTHERE
      @HELLOHELLOISANYBODYTHERE Před 8 měsíci

      indians trying not to mention india in a comment section (impossible) did anybody ask?

    • @Khoon69
      @Khoon69 Před 8 měsíci

      ​@@HELLOHELLOISANYBODYTHEREpain bruh

    • @Its_GtG
      @Its_GtG Před 8 měsíci

      Try to do the mit integration bee finals question also this is only a qualifier question (and btw I am an Indian too)

    • @qwertyuiop2161
      @qwertyuiop2161 Před 5 měsíci

      yeah clearly you aren't too bright.

  • @NaN_000
    @NaN_000 Před 10 měsíci

    Glad to see you back 😊

  • @shadow_1213
    @shadow_1213 Před 10 měsíci

    Outcome: xe^(x^3) + C

  • @vansh3813
    @vansh3813 Před 10 měsíci

    i want more question videos

  • @mohammadalkousa2856
    @mohammadalkousa2856 Před 10 měsíci

    Thanks for video. For MIT integration bee recently it was published a book with solutions to problems of Qualifying Tests from 2010 to 2023

  • @user-bz1wl6iu9b
    @user-bz1wl6iu9b Před 10 měsíci

    Bro where is Minus sign

    • @Khoon69
      @Khoon69 Před 8 měsíci

      Ln 1 is 0

    • @aug3842
      @aug3842 Před 6 měsíci

      he flipped the order from 2,0 to 0,2 which swallowed the minus sign

  • @thevanshff53
    @thevanshff53 Před 10 měsíci

    Bro it's too easy I guess 👍

  • @abhinav21200
    @abhinav21200 Před 10 měsíci

    wow

  • @Infernalith
    @Infernalith Před 11 měsíci

    ln(2) ( i think 😅)