2024 MIT Integration Bee - Finals
2024 ж. 9 Мам.
414 765 Рет қаралды
The integrals and answers can be found at math.mit.edu/~yyao1/pdf/2024_...
Playlist for the full event: • 2024 MIT Integration Bee
Integration Bee website: bit.ly/mitintbee
0:00 Introduction
2:40 Problem 1
8:30 Problem 2
14:20 Problem 3
21:00 Problem 4
27:00 Problem 5
32:30 Tiebreaker introduction
33:30 Tiebreaker problem 1
39:20 Tiebreaker problem 2
45:00 Tiebreaker problem 3
50:50 Tiebreaker problem 4
56:40 Tiebreaker problem 5
1:02:20 Lightning round
If I watch it in reverse, it will be a differentiation competition 😂
copied comment from last years' finals video lol
dog
very funny original joke
😂😂
Bruh 😂😂😂😂
I'd love a commentator duo on these competitions. Find a play by play caster to hype it up and get a professor for a color caster to give explanation and analysis on the integration.
That would genuinely be entertaining
They used to that for these events.
They used to do that. Wonder why they stopped. 🥲
Commentator is a no cause it'll make them hard to focus
They need to focus dude
“I don't integrate the question, l differentiate the options” ~Ме
Based and multiplechoice pilled
Do it in definite integrals 😂😂😂
38:56 "It is hard, it is hard!" 😄
56:01 😂
I know you
Hard...I couldn't even muster the courage to put up my pen for this 😂
omg you are here too
Bprp
PLEEEASEEEE get commentators back on for these videos! There was an earlier Integration Bee with commentators that I managed to learn a lot of different math from, because of the step-by-step walkthroughs. It was like a sports event, but with integrals!
is there a link for the one with commentators?
MIT almost seems like an alternate reality. A world where students gather to compete in integration (as if it were a sport), and where everyone is involved in something extraordinary to push the boundaries of human knowledge. Amazing ✨
Copied 😂
dont bruise ur throat too hard
Glazing for these pupils is BEYOND WILD 😢😂
U trying so hard to get in bruh
@@bobabola2206 alright bro calm down, its not that serious
We're so back
The red shirt sitting in the 3rd row is the JEE Advanced 2020 AIR 1 and an IOAA 2019 gold medalist; hes also won the bal shakti puraskar, the highest honor achievable as a teen in India. Also, the guy in the light green shirt @ 2:18 is the only 2 time winner of mathcounts; and a 4 time IMO gold medalist; not to mention he also won the MIT integration bee 2023; potentially one of the best mathletes in the world. Luke and Brian also secured the top spot at the 84th Putnam math competition. This room has some truly incredible brains 🌟
wow, you know so much! how do you know these?
@ronaldwings5521 it's just that I was really interested in these type of things throughout my last 4 years of high school, so thoroughly researched math competitions and watched various interviews, and over time, knowledge build up
Chirag Falor
is pranjal srivastav also in mit intregation bee ?
@@scienceium5233 nope not in this one, but i really do hope he shows up for at least one of these, obviously hes a very accomplished math olympian but i wonder where his calculus game is at
3 2 1 İntegrate! I love this starting.
commentary would make this slap, even if just for finals?
like the MIT 2006 integration bee
They need to focus abeg
@@flashyred9125obviously the commentary is just for the 1.6 million people watching the video
sLaP
Loving this. Please continue this every year
The step up in difficulty is amazing. The first round I got most. The quarterfinals I got less than half. The semifinals I got just two. This round, apart from the lightning trio, I literally just got tiebreaker #3. These guys are wild.
Did you do it all while being timed though?
@@a.b3203 yes, otherwise I might have (or might not have) got more.
You're wild also bro
bro you got that beast!
@@inevitable1222 here's the trick for tiebreaker 3. When you add the coefficients, you get 0, so 1 is a root, meaning x-1 is a factor. After algebraic long division, that works twice, so (x-1)² is a factor, and (x-1)² √(quadratic) is much more doable, with trig subs and so on.
I only went up to pre calc in school.(which i failed by the way lol). so this is way over my head, but im just a fan of people doing difficult stuff. and this is awesome! Thanks for recording and sharing!
i genuinely love this
I saw this live last month it was so cool
Loved every bit of this! I’m actually out sick and have taken the week off from work, but man this is so so good! 😌 Can’t wait for next year I guess!
Thank you for the recap, your assumptions were correct
My toxic trait is thinking that I can beat these students after just learning the calc 2 integration techniques a few days ago 🤣🤣🤣
real
learning this is ap rn and thinking I can do them too
lmao same
Same but I’m currently learning them now
I think Chirag will easily beat them but I was wrong😢😢 Cause these problems are way easier than the JEE perspective and Chirag Falor had AIR 1 in JEE
Problem 5 is really interesting. I would not have thought that you could disguise a combinatorics problem as an integral in that way.
Wow Calc 2 as a hobby and math contest. Calc 2 in first impression beat me back in 2020 spring but I am excited to learn it as a hobby until ready to take the class.
this year problems were harder, no surprise first 4 haven't been solved. I did third one with 2 different ways but it seems unreal to get to answer in 5 min
3,2,1 integrate Me:Yes
😤🤌
Please continue.
it’s new competition. so interesting and exciting
Would be 10/10 if it had a commentator. Hype it up to all KZheadrs like me that knows shit about math but just want to watch some crazy shit before going to bed
I've been watching these bees for three years now (was a little late on this lol). Applied for MIT this academic year. Hope I get in. This type of culture is something I would be forever happy to engross myself in for the rest of my days. 😅
Did you ever get in?
@@xygomorphic44 how old do you think this comment is lmfao
@@xygomorphic44 I wouldn't know yet. I just made this comment 2 days ago after all.
@@thesecondderivative8967good luck.
you guys are great mathematicians!
Man I love how people has the opportunity to be in these universities, I'm from Argentina and could never dream of something like that, be proud of having the opportunity to at least participate to study there, I'm proud of my opportunity to study, too. But it's just so amazing to be able to study there. Well, anyways I'm happy that there's internet to access free resources
proud of myself i solved the last integration question in 5 secs
@Muita-Informacao i can make a vid on my yt explaining how to solve integrals easily if you want ?
I am glad I did it in 20 seconds lol. Barely remember the trigonometry formulas.
@@JujutsuMathyes please
I am better than you, I solved the last question when they showed the first question.
lets go bro thats sick@@KDYinKZhead
The ln(2e^x-1) /(e^x -1) could be done by feynmans trick......nice to see such a fun competition, I wish it was open to outsiders as well haha, they look too fun to solve!!!! Love the energy of the room
Where should the parameter be placed ?? I can't do it
i got 2lnx/(x^2-1) now what to do
there is no energy in the room lol
@@armansrivastava1055 integrate that by parts
Its really interesting to watch
Luke Robitaille 😢 Never forget
I like how i see this viedeos without knowing the basicals of integration, i'm just existing, and trying to figurate how did i would to do this without the time limit.
damn luke didnt make it to finals. still see him having a fun time in the audience :)
participants don’t allow to use Algebraic Regularization on 1/x^n term? 😢
First problem can be done by parts but we need to produce derivative of inside of denominator as factor of numerator Tiebreakers Problem 3 Factorize expression inside square root
happy to see that chirag falor bhaiya got upto. the 2nd level
YOU NEED A COMMENTATOR FOR THIS.
second is 1/2. logx/x is 1 so take 2 outside as common. done.
These are great
If you play the video in reverse it becomes Differentiation bee
"You are off by a constant factor" after 2nd .. made me laugh so hard 😂😂😂😂😂
13:42 seeing him miss by just 2 on the denominator caused me physical pain
I literally said out loud NO
I love it ❤ the cocept is too much hilarious as a student of calculus who has it is own struggles with it, but they did it 5 min for integration what a competition ia it to participate😂😂😂
Can I join this tournament if I've only taken AP calculus AB?
Need to take Calc BC
Really bro !!!! Did u guys just click for going to next page in pdf !!!! @MIT
3,2,1,integrate is the most funniest line i have ever heard
Here before this blows up
Omg I am done with problem 1 😤😤 1. Denominator sin(x+53°) 2.x+53°=t By parts integrate
50:32 "do you guys want a break?" Both competitors: 🤷♂
Nooo, on the second problem, the guy put e at the bottom of the integral instead of 1 after he did u substitution and rewrote it. That’s a simple mistake
And even this year one of the top universities of the world cant develop a program to change the page and start the timer simultaneously! 🤦♂
one day I'll be there competing in this
"The test's gonna be easy, its your first mock :)" the test:
I would like to see how to solve the first one
GO BRIAN!!
bro chirag falor(iitjee rank1 2020) was on semi final #1 with Brian Liu ....
No square root by parts , ?
This is where I belong❤
simultaneously sad and glad all my college math skills are gone
Currently experiencing college PTSD flashbacks from Calc 2
it would be better if the timer was shown all the time, while they're solving, it adds to the suspense of the video
Engineering is the Ellison of science
Tell me after graduating from college they get salaries for solving questions instead of doing coding in IT companies
Anyone else fast forward though the work to see if their answers are correct 😂
You guys really need to make a serious pitch to the IOC to make this an Olympic Sport. This is blood sport. This is up there with brutal events like the decathlon, cross country skiing, single skull, 50km walk, 400m hurdles and marathon.
I fucking love this- Asian host dude is awesome- yes get some commentators who are experts to provide play by play -
Well done Brian, I rooted for the wrong person with the letter b i guess 😂😂
CHIRAG FALOR , the legend is in there
Twitch stream with commentators next year pls!
Compute the Integral x^2024/(x^2+1)^2023 dx
Take x²+1=t
Do my exercises, please.
@@Rithida.Math2024 use substitution
*53:49* Bro's remembering the days of y = mx + b ☠☠😭😭
The wars that we should be fighting…
Watching directly final
Almost feels like the world where I wanna be but will never make it like an really far fetched reality
Need a gaming announcer over this it’d be the most entertaining competition 😂
Haha … integration bee … • can u use it in equation? • I would like to phone a friend
Rank Number 3 Chirag Falor - JEE ADVANCE AIR 1 2020❤❤❤🇮🇳🇮🇳🇮🇳
1:07:36 Bro is shaking, hope he is alright.
Dont know why but these are in asia high school and mine isnt an exception😂
any one noticed AIR 1 Chirag Falor was in Semi Finals
Can ya provide me the link
Yeah i know, he should be because he has solved these questions before
The one who Wins, gets the cheerleader
yes i can do ALL of this in my sleep with both of my eyes open and years of study and my death
i want to attend one of these so bad but never got the chance to apply to mit :(
same 😭
Harder calculus problems than l used to solve
Wanted to see chirag 😢 but these people are so insanely talented holy shit
Yeah
Hey Evan Tanko !
+C
2:19 I thought the guy in black without the bucket hat is the other competitor
xD the real winners are probably the one's who set those questions
Those are the teachers i guess
Messi vs Ronaldo … I can barely hear Messi’s chalk scratch the board 🤣🤣🤣🤣
Did anyone noticed chirag falor name in the list 😊😊😊
Not five minutes, 04:57 only.
does anyone know how to do the one with the max which is 4/11 at the end please ?
The inner expression involving the floor functions is equal to 1 if {2^n*x} < 1/4, otherwise it is 0 (where {2^n*x} denotes the fractional part). Write x = 0.b₁b₂b₃... in its binary expansion. We want to find the least nonnegative integer n such that {2^n*x} < 1/4. If it exists, then (1/2)^n is the value of the integrand at x, otherwise it is zero. Let's say that x ∈ A_n for 0 ≤ x < 1 if and only if n is the least nonnegative integer such that {2^n*x} < 1/4. Note that given x = 0.b₁b₂b₃..., we have {2^n*x} < 1/4 exactly when b_n = b_(n+1) = 0, so x ∈ A_n exactly when this is the first occurrence of two 0s in a row in the binary expansion of x. Thus, x ∈ A_n if and only if x = 0.b₁b₂b₃...100..., where b_n = 1 and b_(n+1) = b_(n+2) = 0, and the string of digits b₁b₂b₃...b_(n-1) does not contain a 00. Now observe that the integrand is equal to (1/2)^n over each A_n, so we can use Lebesgue integration to evaluate the integral. To do this we need to find the measure of each A_n. The digits after 100 in the binary expansion 0.b₁b₂b₃...100.... do not matter, so we can split [0,1) into intervals of length (1/2)^(n+2) and identify which belong to A_n. These are exactly the intervals for which b₁b₂b₃...b_(n-1) does not contain a 00, and the number of these is equal to F(n+1), where F is the Fibonacci numbers. So A_n consists of F(n+1) intervals of length (1/2)^(n+2), so that the measure of A_n is F(n+1) * (1/2)^(n+2). Now we can evaluate the integral. We get the sum over n ≥ 0 of [(1/2)^n * F(n+1) * (1/2)^(n+2)], which is equal to the sum over n ≥ 1 of [F(n) * (1/4)^n]. The generating function defined by the sum over n ≥ 0 of F(n)z^n is given by z/(1-z-z^2). Since F(0) = 0, we can plug in z = 1/4 to get 4/11.
@@Zephei Yes. Finally you understood. Good job!
how do people even go about learning to be able to integrate things on this level?
I think they talk to their professors and ask them questions about this stuff. They can also be math majors and they learn this in their classes.
@@Potato-so6zr thanks for the response! im gonna be a freshman in college this year and they do an integration bee so i wanted to start preparing
They are IMO gold medalists for starters
wth the last integral looked so demonic LOL I can't believe they did it under 1 minute wtheck
Bring commentators back!!
crazy
was able to solve only one 😢
If this is the "new" math, I can see why kids are flunking their SATs.