MIT 2006 Integration Bee

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  • @OfficialSilverMoon
    @OfficialSilverMoon Před 4 lety +7572

    You're not deaf, audio starts at 00:32

  • @StudiosAdVanced
    @StudiosAdVanced Před 5 lety +10416

    other colleges: at parties
    MIT:

    • @guthries
      @guthries Před 5 lety +351

      I went to Michigan Tech and we did this at our parties.

    • @MonteLogic
      @MonteLogic Před 5 lety +9

      😂😂

    • @marshmelows
      @marshmelows Před 4 lety +4

      wooooooo

    • @Aserve1st
      @Aserve1st Před 4 lety +126

      theyre partying in their brain.

    • @uristmcary
      @uristmcary Před 4 lety +65

      im down, beats sitting around wondering when you can go home without making your friends feel sad and lonely.

  • @unknowno_o8220
    @unknowno_o8220 Před 2 lety +256

    They really made some of the most traumatic experiences of my university career into a sport. They really built different.

  • @thenextkawhileonard2585
    @thenextkawhileonard2585 Před 3 lety +642

    Her: he's probably out cheating on me
    Me and the boys:

  • @ignaciodemiguel3683
    @ignaciodemiguel3683 Před 4 lety +8656

    "Hey, Keith, don't forget to upload the Integration Tournament to CZcams."
    "Yeah sure, I won't forget."
    *10 years later*

  • @n00bspanker
    @n00bspanker Před 4 lety +2030

    "I'm sure most of our viewers would be familiar with [insert mathematical concept here]"
    Me: "Yes. Absolutely. Entirely."

  • @chrisw3869
    @chrisw3869 Před 3 lety +117

    This is the most intently I've ever watched something where I can't even begin to comprehend what's happening.

  • @ComposingGloves
    @ComposingGloves Před 3 lety +449

    I was in an ODE class, where the entire thing was kinda like this but without intentional competition. At any point (even in the middle of lecture) you could go up to the board and present an idea, if your insight was good you got extra credit. It wound up being one of my favorite classes. Every day was exciting and I devoured the material. I still use it and remember most of it because of that method. The teacher was a legend.

    • @ninjahunterx7497
      @ninjahunterx7497 Před 2 lety +1

      That's amazing.

    • @RubyByte
      @RubyByte Před rokem

      What the fuck are you talking about

    • @epicm999
      @epicm999 Před rokem +1

      If I ever teach a class, I'm gonna steal that.

  • @orangeboy97
    @orangeboy97 Před 5 lety +4690

    17:24 "small mistakes crash rockets into planets"
    I'm going to say that the next time my physics professor makes a mistake.

    • @ozancanca9740
      @ozancanca9740 Před 5 lety +16

      Tall Random Guy me too lol

    • @joelbachul924
      @joelbachul924 Před 5 lety +11

      I was about to comment this LOL 😂 that was hilarious

    • @eggshells652
      @eggshells652 Před 4 lety +12

      Tall Random Guy small mistakes cost lives and millions of dollars

    • @jeanmichel4269
      @jeanmichel4269 Před 4 lety +7

      hopefully everything is now calculated with a computer

    • @user-bp8yd7uy6h
      @user-bp8yd7uy6h Před 4 lety +17

      And so he'll say when you fail your test 🤣🤣

  • @Gametheory101
    @Gametheory101 Před 8 lety +3992

    The integration is pretty fantastic, but what amazing video quality for an amateur 2006 production!

    • @KeithWinstein
      @KeithWinstein  Před 8 lety +749

      +William Spaniel Thanks! This was done by the MIT Sportcast HD project, which we understand to have been the first amateur HD broadcasting anywhere. The video came in over Ethernet (translated from Firewire) from four HDV cameras, and was edited and encoded live to meet the ATSC requirements using software we developed on Linux and OpenGL, then broadcast on MIT's internal cable-TV system in 2005-2006. (sportcast.mit.edu)

    • @99bits46
      @99bits46 Před 5 lety +66

      @@KeithWinstein truly amazing..

    • @pablodeagustin5404
      @pablodeagustin5404 Před 5 lety +95

      its MIT, what do you expect ?

    • @itzyoung
      @itzyoung Před 5 lety +19

      @@KeithWinstein 1:20:33 , pretty amazing for the time!

    • @vikvc
      @vikvc Před 4 lety +31

      @@KeithWinstein While many teachers around the globe still struggle to plug a computer to a projector.

  • @tonywoo4861
    @tonywoo4861 Před 3 lety +144

    I love how the commentators make legit comments about integration. Absolutely amazing.

  • @voguelactose9468
    @voguelactose9468 Před 2 lety +194

    Even as someone who never went past differential calculus in school, this is one of the coolest things I’ve seen in a long time. The concept of an integration tournament, complete with a commentator and a very enthusiastic and excited audience is just so awesome .

  • @bhartiranjana3087
    @bhartiranjana3087 Před 4 lety +2949

    Did i really just watched 3 hours long integral bee instead of solving my homework on differention first

  • @NeverLooksAtComments
    @NeverLooksAtComments Před 5 lety +8103

    ok that commentator is insanely talented... he had to know what he was talking about, and he had to keep talking, and he was able to make it extremely entertaining/informative and easy to follow.

    • @edwardguterres8964
      @edwardguterres8964 Před 5 lety +166

      NeverLooksAtComments he’s my dentist lol

    • @user-qi6ig6gb8x
      @user-qi6ig6gb8x Před 5 lety +43

      @Phytom try an integral before you die, or you'll regret :haha

    • @nuklearboysymbiote
      @nuklearboysymbiote Před 5 lety +80

      well yeah they said they wrote some of those integrals so obviously they knew what they were talking about

    • @gwub7117
      @gwub7117 Před 4 lety +58

      as a math nerd, differentiation was nice but integration was the cherry on the top

    • @vinnerzucc1154
      @vinnerzucc1154 Před 4 lety +6

      Edward Guterres what’s his name

  • @NoGoodHandlesComingToMind
    @NoGoodHandlesComingToMind Před 3 lety +173

    1:54:40, "facing the guy *who took 6 rounds to get an integral*."
    Me having no idea what's going on: "Yes, an amateur, how pathetic..."

  • @starlordstarlordman8489
    @starlordstarlordman8489 Před 3 lety +48

    I would love to know where the commentators are today. I am loving this, 15 years later. Better commentating than most sports events. Great video all around, thanks to all involved.

  • @AAA11546
    @AAA11546 Před 5 lety +835

    The commentators are fucking great. The way they explain what the guys are doing, what method, what it means. wow. this is actually interesting

  • @TrinadhV
    @TrinadhV Před 4 lety +410

    New roommate: So, what sports do you like to watch on TV?
    Me: .. it's complicated.

  • @hywei5171
    @hywei5171 Před 3 lety +83

    MIT students: do integral the old fashion way
    Me: google "integral calculator"

    • @234AaronSuper
      @234AaronSuper Před 3 lety

      no cap haha

    • @JasonJia11
      @JasonJia11 Před 3 lety +9

      some of the extreme integrals couldn't even be solved by Symbolab or Mathway

    • @nathandrake711
      @nathandrake711 Před 3 lety +1

      Sometimes an integral will have multiple answers all correct

    • @navjotsingh2251
      @navjotsingh2251 Před 3 lety

      @@JasonJia11 almost all numerical integrals and derivatives can be computed using online calculators. But, there are certain symbolic math problems which computers cannot do (though, there is research in the field of using machine learning to help computers do symbolic math the same why humans do but idk how well that’s going as I don’t kept up with the field)

  • @bonbon_1729
    @bonbon_1729 Před 3 lety +23

    This one video has helped me be more eager to learn maths. I know it’s old, but I thank everybody involved.

  • @KurdTillDeath
    @KurdTillDeath Před 5 lety +5316

    ha... what a bunch of nerds...
    wish i could do that

    • @prabalbaishya6179
      @prabalbaishya6179 Před 4 lety +143

      If you really wanna learn about calculus, then there are plenty of good calculus videos in CZcams. Believe me what they are doing, you can too! you just need to learn about them and then keep on practising :)

    • @crismal6477
      @crismal6477 Před 4 lety +12

      Prabal Baishya that is very true

    • @crismal6477
      @crismal6477 Před 4 lety +10

      Prabal Baishya I’ve learned that way, lol
      And also through websites

    • @avegaughtastiffy1654
      @avegaughtastiffy1654 Před 4 lety +16

      It’s really about applying the rules

    • @valt1337
      @valt1337 Před 4 lety +6

      but can they fight or invite a girl out?

  • @alexandervu8693
    @alexandervu8693 Před 5 lety +2815

    Was I looking for a 3hr video on integration? No
    Did I watch it? Hell yeah

    • @alexandervu8693
      @alexandervu8693 Před 5 lety +26

      Throngdorr Mighty yep, im a future math/physics major so it was enjoyable watching others attempting challenging integrals as well as alternative ideas to approach a problem

    • @dibyashubhroroy945
      @dibyashubhroroy945 Před 4 lety +3

      @Throngdorr Mighty ya so is integration

    • @learninggreek501
      @learninggreek501 Před 4 lety +1

      hell yeah thats the spirit!

    • @tauceti8341
      @tauceti8341 Před 3 lety +3

      @@alexandervu8693 the first hours was bad no one could solve their integrals, poor lads.

    • @bigbuilder10
      @bigbuilder10 Před 3 lety

      @Throngdorr Mighty ???

  • @mandymcfadden584
    @mandymcfadden584 Před 2 lety +72

    How wonderful the world would be if everyone spent their time in such pursuits. Beautiful, happy, intelligent, wholesome people.

  • @vihashah5975
    @vihashah5975 Před 3 lety +25

    commentator: "someone's gonna get this",
    Li Yu and Ross: we can do this all day...

  • @Meta-Drew
    @Meta-Drew Před 3 lety +383

    "They haven't been able to get the first 5 problems"
    *Me on my 5 question Calc test*

  • @brianchang408
    @brianchang408 Před 6 lety +2556

    imagine if there was a professional league for this.....

    • @xDosReis
      @xDosReis Před 6 lety +223

      there are people who could integrate these in their head in two seconds

    • @jaronfeld123
      @jaronfeld123 Před 5 lety +285

      Not really. This is hard stuff. There aren't people who are trained to do these complicated integrals professionally. MIT kinda has the best undergrad integration experts.

    • @jmika5984
      @jmika5984 Před 5 lety +36

      51:02

    • @cappuccinopapi3038
      @cappuccinopapi3038 Před 5 lety +12

      The world world would be a better place

    • @chizurin6357
      @chizurin6357 Před 5 lety +3

      @@jmika5984 That integration was really simple and easy

  • @lariosphotography4721
    @lariosphotography4721 Před 3 lety +29

    I really appreciate this bit from the commentators
    "...not the pressure of some sort of timer winding down. That's not math. That's sports, isn't it?"
    "that's Apollo 13, maybe."
    I think both commentators have a good point here. On the one hand, yes, some mathematicians/physicists should be able to work well and efficient under pressure. However, some mathematicians can be assigned to certain problems that are not so immediate.

  • @nathan87
    @nathan87 Před 3 lety +81

    3:00:09 "Hearing your opponent's chalk clicking against the board it's gotta play into your mind a little bit there"
    "Yogash has simply written the problem..."
    relatable

  • @jkershenbaum
    @jkershenbaum Před 3 lety +856

    Do the students down the hall in the MIT laser lab have a disintegration bee?

    • @kushalsb460
      @kushalsb460 Před 3 lety +66

      differentiation is too easy to have a competition, I guess.

    • @gautam2034
      @gautam2034 Před 3 lety +4

      Kushal Bastakoti chutiye

    • @rubricscube_
      @rubricscube_ Před 3 lety +4

      I chortled

    • @frogstereighteeng5499
      @frogstereighteeng5499 Před 3 lety +5

      No diffeqs? There would be some fun ones there lol.

    • @MoonlightMirage
      @MoonlightMirage Před 3 lety +10

      @YouBuet Trust me, a woooosh ain't needed around here :p
      Differentiation is definitely easier than solving integrals

  • @danilocorreia5104
    @danilocorreia5104 Před 5 lety +3378

    Now I know why I wasn't accepted at MIT

    • @Junzipark8881
      @Junzipark8881 Před 4 lety +292

      Danilo Correia yes judging by your sentence we can all tell why you were rejected from mit

    • @jeeaspirant6288
      @jeeaspirant6288 Před 4 lety +249

      @@Junzipark8881 shut up kid

    • @silvergg8152
      @silvergg8152 Před 4 lety +398

      @@Junzipark8881 Cause he misused the preposition "on"? Kind of ironic considering in your sentence "by" would be more appropriate than "from".

    • @Junzipark8881
      @Junzipark8881 Před 4 lety +37

      I Like Pie how is it ironic? He completely butchered the sentence lol I dont like pointing out grammatical errors online because obviously no one cares enough when they post comments; however, if someone is going to make a comment on why he was not accepted into a prestigious school and completely butcher the sentence, I am going to point it out. I mean it was kind of a joke in the first place, he probably didnt even apply to mit lol

    • @Junzipark8881
      @Junzipark8881 Před 4 lety +12

      harsh tripathi alright man it was a joke in the first place because he probably did not apply to mit in the first place

  • @billydoan6153
    @billydoan6153 Před 3 lety +132

    As a Mathematic Grad student, I am very jealous of those guys' talent, good job. Wish I could be as smart as them. Watching this whole thing while doing my research really boost me up. Thank you, cheer! =)

    • @akshatsharma8151
      @akshatsharma8151 Před rokem

      Indian high school students writing the entrance for the IITs are way more intelligent than them.

    • @user-uh9bo2im1h
      @user-uh9bo2im1h Před 10 měsíci +3

      Dude you’re math grad students you’ve solved integrals so much harder than this one and honestly math 505 has some good integrals to look into

    • @DeadPool-nx3gy
      @DeadPool-nx3gy Před 8 měsíci +1

      Some of these were soo easy 👍

    • @tobiasmelgard2070
      @tobiasmelgard2070 Před 5 měsíci

      ⁠@@DeadPool-nx3gyGood for you my guy

  • @abhinavcheedella4296
    @abhinavcheedella4296 Před 2 lety +10

    It’s crazy that when I first saw this, this was some crazy math shit but now i actually understand it all

  • @tedubadu2536
    @tedubadu2536 Před 5 lety +468

    When the Athletics Dept is involved with the integration bee, you know it's a tech school.

  • @davemonkey26
    @davemonkey26 Před 4 lety +741

    "Not a bad crowd here tonight, gotta be at least 60-70"
    *Laughs in 619,000 views in 2019*

  • @NASAFanboy
    @NASAFanboy Před 2 lety +46

    As an engineering student, thank you for reassuring myself that I’m going into the right area of study. I just watched the entire thing and enjoyed every second of it, great video and concept!

  • @forgetfulfunctor1
    @forgetfulfunctor1 Před 2 lety +6

    Rumor has it that every time someone posts an integration bee video, 1000 IIT JEE applicants leave their studying lair to go comment how easy it is

  • @pharmacist66
    @pharmacist66 Před 4 lety +261

    bro go to sleep man you've been on youtube too long

  • @prateek16
    @prateek16 Před 3 lety +221

    The dude with no shirt on showed up at the wrong party

  • @ezuki6774
    @ezuki6774 Před 3 lety +29

    "this is Sport Cast at MIT." 5:18 im wheezing

  • @leomurry8195
    @leomurry8195 Před 2 lety +20

    I just got an A in calc 2 at a public university and thought I would follow along with this competition to see how I compared. After getting exactly 0 correct and having to google what cosh was, I am incredibly humbled.

    • @EPlTHANY
      @EPlTHANY Před 2 lety +4

      How do u get an A in calc 2 and not know what cosh is lol

    • @leomurry8195
      @leomurry8195 Před 2 lety +13

      @@EPlTHANY My calc 2 literally never covered it. Also I knew it was a thing, but I didn’t know exactly what it was until I looked it up

  • @BlijVrouw
    @BlijVrouw Před 4 lety +631

    They're definitely trolling us by calling these "trivial" or "easy" integrals.

    • @r1ultramax
      @r1ultramax Před 3 lety +32

      No they are actually easy.

    • @ezu8501
      @ezu8501 Před 3 lety +8

      they are easy...

    • @timewalker6654
      @timewalker6654 Před 3 lety +16

      Trivial means classic

    • @KayOScode
      @KayOScode Před 3 lety +19

      They arent too hard, but they require tricks

    • @bait5257
      @bait5257 Před 3 lety +2

      Um yes they are actually

  • @FruchteisMitErdbeer
    @FruchteisMitErdbeer Před 4 lety +3144

    This is absurdly well produced. Good camera quality for the time, great commentary, good shots and camera work in general. Good audio , even being able to hear the audience and contestants well. Legit, professional sports broadcasts can take note from this.

    • @nuklearboysymbiote
      @nuklearboysymbiote Před 4 lety +73

      This is the only good MIT integration bee video I can find. Any other years' videos as high quality as this?

    • @SqueeblesMcklooflin
      @SqueeblesMcklooflin Před 2 lety +12

      I would rather watch these than sports any day

    • @barte6128
      @barte6128 Před 2 lety +12

      Can’t believe this was made in 2006, Windows XP era

    • @wristocrat
      @wristocrat Před 2 lety +8

      Yeah these guys should really consider going into a field with technology in it considering how good this video is

    • @TacosYBurritos8P
      @TacosYBurritos8P Před 2 lety +1

      2006 was not the 1960s either

  • @Ifoundthelight1
    @Ifoundthelight1 Před 3 lety +9

    These are the people your math problem tells you not to worry about.

  • @Gamezilla00
    @Gamezilla00 Před 3 lety +4

    The commentary really made this thing what it is. Surprisingly I watched through it all and quite enjoyed it lol

  • @AlwaysBeWater
    @AlwaysBeWater Před 5 lety +1133

    Somewhere in that crowd, someone is solving all these in his/her head.

    • @kataeiautsav918
      @kataeiautsav918 Před 4 lety +159

      but that someone wasnt able to clear the test to be selected for this event

    • @Victor-ji1rz
      @Victor-ji1rz Před 4 lety +39

      Utsav kataria or didn t try

    • @bensblues
      @bensblues Před 4 lety +140

      no there isn't. Integration isnt like that.

    • @tahademirkan8567
      @tahademirkan8567 Před 4 lety +53

      His name is Will Hunting

    • @bensblues
      @bensblues Před 4 lety +32

      @@nukemars9445 I find it highly unlikely Nikola Tesla is sitting in that crowd considering he died over 70 years ago...

  • @backlog2389
    @backlog2389 Před 3 lety +562

    This is honestly such a genius idea. Its an easy way to get your students extremely comfortable with integration for the higher level courses.

  • @mathisnotforthefaintofheart

    As a mathematician myself, I enjoyed this video and frankly speaking, I learned some stuff from it as well...

  • @SSJVNN
    @SSJVNN Před 3 lety +2

    This was so good lol. It's strange/sad but I felt very good/warm vibes from this video+ the comments section. I wonder what David Xin is doing now

  • @rahilsanghavi9347
    @rahilsanghavi9347 Před 4 lety +720

    The thing I loved the most is that the commentators know what they are talking about...they seem to be MIT integration bee veterans

  • @johndanielvillanueva8604
    @johndanielvillanueva8604 Před 3 lety +7

    I can't believe I watch all three hours of this without getting bored. HAHAHA

  • @nathanschmidt7662
    @nathanschmidt7662 Před 3 lety +18

    Must be so cool to arrive into the MIT community as a bright (maybe socially isolated) ~18 year old. Suddenly you're among others who can discuss mathematics and play around with algorithms together for fun.

  • @christianblake2179
    @christianblake2179 Před 3 lety +646

    Very few hold the title of “Grand Integrator” at MIT and this legend is one of them

  • @mathmaniac3033
    @mathmaniac3033 Před 3 lety +776

    Timestamps for rounds (for my own benefit later lol):
    Introduction and Proceedings: 00:00:32
    Round 1, Elimination: 00:06:43
    Round 2, Elimination: 00:47:40
    Round 3, Quarterfinals: 00:53:23
    Round 4, Quarterfinals: 1:10:27
    Round 5, Quarterfinals: 1:26:37
    Round 6, Quarterfinals: 1:50:21
    Round 7, Semifinals: 1:58:27
    Round 8, Semifinals: 2:27:00
    Round 9, Runner-up: 2:44:47
    Round 10, Finals: 2:55:24
    Awards: 3:10:40
    What a great event to watch. Loved that final round!

  • @iuvdisuhb-ld3ou
    @iuvdisuhb-ld3ou Před 2 lety +4

    the commentators know that some of the integrals at the start were genuinely quite simple, but thats the thing about integration, under even a little but stress you make mistakes and there are so many levels to the integral that going back and finding it seems like such a huge task. personlly i think that among the first 5-6 integrals, they should've gotten atleast two of them correctly. and the left contestant wrote '0' as the answer to the definite integral and the commentators were like, thats not an odd function buddy and neither are the limits. great fun!

  • @champagnebaby4184
    @champagnebaby4184 Před 3 lety +1

    I really fell a sleep watching CZcams and woke up in the morning to this😂

  • @davidvalle3068
    @davidvalle3068 Před 6 lety +439

    I felt bad that I couldnt solve these, but then flet better when they couldn't either

    • @jeevansamrudh5600
      @jeevansamrudh5600 Před 5 lety +11

      those were pretty easy , wonder were they mit graduates or not

    • @EDROCKSWOO
      @EDROCKSWOO Před 5 lety +99

      @@jeevansamrudh5600 yeah sadly you cant do in front of an audience or in the given 3 minute frame, because you would get nervous, write nothing, and get humiliated Lol.

    • @mridulbhatt8917
      @mridulbhatt8917 Před 5 lety +26

      @@EDROCKSWOO they are nerds anxiety comes with high intelligence

    • @bee_irl
      @bee_irl Před 4 lety +3

      @@mridulbhatt8917 Anxiety comes with high intelligence?

    • @nanni5230
      @nanni5230 Před 4 lety +1

      @@bee_irl It's not proven but a lot of "geniuses" tend to have anxiety in some sort of capacity.

  • @Steveiegaming
    @Steveiegaming Před 6 lety +379

    gotta love the dude with the double integral face paint

  • @jasminenissen7169
    @jasminenissen7169 Před 2 lety +1

    I'm not sure how I ended up here from watching motorcycle engine repair videos to this especially since I struggled a lot with calculus last year but this is insane to watch!

  • @joelnord4699
    @joelnord4699 Před 3 lety +5

    There's something cathartic about watching MIT students make simple math errors

  • @YangWangPhD
    @YangWangPhD Před 3 lety +188

    This needs to be on ESPN. Where's the 2007 season?

  • @ziggystardust6566
    @ziggystardust6566 Před 5 lety +651

    3:48 dudes got binoculars lmao

  • @Cnightz
    @Cnightz Před rokem

    The commentary kept me interested even though this is above my skill level. Happy I stumbled on this video. Learning is always exciting.

  • @unreligeouspope7902
    @unreligeouspope7902 Před 3 lety +7

    I have a geopolitics paper due next week, this research is quite helpful!

  • @ahnafsamin4507
    @ahnafsamin4507 Před 5 lety +830

    1:18:47 the guy on the right is my situation

  • @christianmcclaine9990
    @christianmcclaine9990 Před 3 lety +82

    I never thought I would hear the word "extreme" next to "integral"

    • @gabedarrett1301
      @gabedarrett1301 Před 3 lety +2

      Pretty much every integral is 'extreme' to me lmao. That's why I solve my integrals numerically

  • @flygonfiasco9751
    @flygonfiasco9751 Před 2 lety +7

    The pressure must have been crazy, some silly mistakes from the first two contestants, but under normal conditions you can tell they’d do some of these with no problem

  • @FellatioHoratio
    @FellatioHoratio Před 3 lety +10

    How do they have seeding lol, is it based on exam scores

  • @karanchotaliya1714
    @karanchotaliya1714 Před 5 lety +346

    3:00 AM Always leads me to weirdest place.

  • @trebvvv
    @trebvvv Před 5 lety +77

    I like how the commentator keeps going "okay, one of them HAS to get this one", and then they don't for like 5 straight.

  • @ab3040
    @ab3040 Před 2 lety +8

    Commentator has to be some kind of a PHD student
    Really knows his stuff while still being more entertaining than a professor

  • @Maxmuetze
    @Maxmuetze Před 2 lety +3

    2:07:10 is done by symmetry, as the commentator suggests (but it's still really hard, even just proving the given answer). Tried this again and again and finally got it like this: (All integrals from 0 to pi/2) say I := int log(sin x) dx. Then also I = int log(cos x) dx by symmetry. So 2I = int log (sin x cos x) dx = int log (sin(2x)/2) dx = int log sin(2x) dx - pi/2 log(2). Also, int log sin(2x) dx (again from 0 to pi/2) is actually equal to I, by symmetry of the integrand about x=pi/4 and scale factor 1/2. Subtract equations for 2I and I to get I = - pi/2 log(2)

  • @saurabhgi
    @saurabhgi Před 3 lety +1821

    The commentator is the real mvp/math wiz during the finals.

    • @school6268
      @school6268 Před 3 lety +26

      yeah, guess mit profs are like that...

    • @jaredtweed7826
      @jaredtweed7826 Před 3 lety +11

      The commentator is the camera guy in this video: czcams.com/video/9y7L8kAuPxs/video.html

    • @jerrymemberryoh4816
      @jerrymemberryoh4816 Před 3 lety +6

      @@athena546 was mmm

    • @Bigaznboo010
      @Bigaznboo010 Před 3 lety +1

      D I itI’ts YI eah that’s @@athena546 ir I’m okay good good job buddy hope hope you’re ok

    • @Bigaznboo010
      @Bigaznboo010 Před 3 lety +1

      Dfddffffffdfffffff

  • @metrictensor9745
    @metrictensor9745 Před 6 lety +570

    There MUST be a competitive league for this (Or maths). The casting makes this SO SICK

    • @MrCmon113
      @MrCmon113 Před 5 lety +5

      There is lots of maths competitions. Not live events though.

    • @natefcod9361
      @natefcod9361 Před 4 lety +15

      @@MrCmon113 would've been cool if they were live broadcasted like this with a comentator

    • @cheesywiz9443
      @cheesywiz9443 Před 4 lety +3

      @@natefcod9361 this is a speed test with (relatively) easy integrals
      an actual maths test would have integrals that would take you much longer to solve ..and that is if you can solve it in the first place.. watching a competition like that would be like watching paint dry..sure its fun for the competitors and other people that will try out the problem but not so much for the spectators...

    • @alexwang5463
      @alexwang5463 Před 4 lety

      there is. it is called mathcounts countdown national competition

    • @stewartzayat7526
      @stewartzayat7526 Před 3 lety

      @@user-vo8zx1db6m this was, but his point was that usual math competitions would not be.

  • @yuitora8749
    @yuitora8749 Před 2 lety +9

    2:37:04 this one is tricky and has a trap (which Vijay fell for).
    So the idea is to decompose it to "simple fraction", so you get 1/x(e^x+1) - 1/x(e^3x + 1)
    Then intuitively, you'd want to separate into 2 integrals (which Vijay did and he got 0 as answer), but you can't do that because you'd get 2 divergent integrals (because 1/x is not integrable at 0)
    In order to separate into 2 integrals, you first need to do integration by parts (integrate 1/x and differentiate the rest) so that you get ln(x) which is integrable at 0, and then you can split into 2 integrals.
    From there, you do a variable change t=3x to the integral with e^3x+1, and everything simplifies nicely.

    • @yuitora8749
      @yuitora8749 Před 2 lety +1

      another way of solving it, which might be overkill (feymann trick), is to replace 3 by t, then differentiate the integral with respect to t.
      Then by the dominated convergence theorem, you can just differentiate the integrand with respect to t (interchanging differentiation and intergral), then after some simplification you get int{ e^tx / (e^tx + 1)} which gives 1/2t which is the derivative of log(t)/2
      This means the integral (when you replace 3 with t) is log(t)/2 + C, but C=0 when you plug t=1. So the integral is exactly log(t)/2.
      Set t=3 you get log(3)/2.

  • @hunterwolfe9059
    @hunterwolfe9059 Před 3 lety +2

    Somehow I watched about an hour of this without realizing it and I have no memory of it.

  • @mahimshahriar7346
    @mahimshahriar7346 Před 3 lety +82

    Me: notoriously sucking at maths since 5th grade
    CZcams: yeah let's recommend this guy integration bee video from MIT

  • @AAA11546
    @AAA11546 Před 5 lety +232

    44:57 *"Hard to see how that would be zero"*
    savage commentator

    • @ninetales1234
      @ninetales1234 Před 2 lety

      At this part, I was thinking that this might just be a shot in the dark, i.e. if the most common answer to math problems is zero, why not just try zero, if the best thing you're able to do at that point, is guess?

    • @deadlypyre
      @deadlypyre Před 2 lety +1

      @@ninetales1234 but sine is always positive lol

    • @ninetales1234
      @ninetales1234 Před 2 lety +1

      @@deadlypyre act of desperation

  • @blacksapphire5612
    @blacksapphire5612 Před 3 lety +4

    im a sophomore in HS taking geometry, i love having my mind just melt watching these

  • @gulvinbadie
    @gulvinbadie Před 2 lety +5

    it’s literally 3 AM and i woke up to this what?

    • @dyhsehehb6232
      @dyhsehehb6232 Před 2 lety +1

      could u pls explain is there some culture of sleeping with watching yt content or something as there are lots and lots of comments like this??

    • @gulvinbadie
      @gulvinbadie Před 2 lety +1

      @@dyhsehehb6232 hm? im kinda lost sorry but i’ll answer to what i understand
      i personally like sleeping while watching anything tbh, but i dont think it’d s culture or anything lol also most of the time i get sleepy but im too lazy to yk close youtube and put my device away so i just sleep by it some times also accidentally
      moral of the story is that people are jusy lazy, too sleepy or just like to sleep by it! it could be comforting tbh buttttt not the best to do so

  • @zenterno-zt1pl
    @zenterno-zt1pl Před 3 lety +367

    2:51:20
    Interesting battle going on I wonder who is going to wi....
    Cameraman: nah fam look what these guys are up to

  • @sukruti7612
    @sukruti7612 Před 4 lety +82

    I cannot believe I watched the whole thing. Oh my gosh. Kudos to the commentators who kept it engaging.

  • @davidstebbins8002
    @davidstebbins8002 Před 2 lety +4

    the commentator made calculus interesting for 3 hours straight someone give this guy a nobel

  • @neilsawhney7182
    @neilsawhney7182 Před 3 lety +7

    Me staring at these integrals blankly, “wow common they couldn’t get 4 integrals in a row”

  • @abcmc6301
    @abcmc6301 Před 5 lety +91

    2:13:28 *confusion intensifies*

  • @MitchellPorter2025
    @MitchellPorter2025 Před 5 lety +231

    It would be fun to see the faculty version of this. Special functions, grassmann variables, path integrals...

    • @sauercrowder
      @sauercrowder Před 3 lety +40

      Haha, yeah... I know, right? They would totally do those things you said, as we all know.

    • @sethsoarenson7414
      @sethsoarenson7414 Před 2 lety +14

      Back in the day you could come for a professor's job by posing problems to them and seeing if they could figure them out. So this would be a great, and traditional, way of figuring out which math prof gets tenure this year

  • @222MovieMan
    @222MovieMan Před 3 lety +5

    I would get so much anxiety if I had to compete in math, I suck at it and I hate competing....

  • @yawasama8248
    @yawasama8248 Před 3 lety +3

    The amount of chalkdust floating in that room would have had me sent to the hospital

  • @kyoko703
    @kyoko703 Před 8 lety +222

    ESPN: The Square Root of Ocho.

  • @venkatakarthikbandaru8326
    @venkatakarthikbandaru8326 Před 7 lety +460

    Great Commentary.

  • @mymafiavideos3040
    @mymafiavideos3040 Před 3 lety +1

    @2:31:10 His answer was almost correct. Here's why: Divide the numerator and denominator by 25. In the numerator you get 1 and in the denominator you get the following:
    ((3/5) cos x + (4/5) sin x)²
    Let t be an angle such that, cos t = (3/5). Then, sin t = (4/5) and tan t = (4/3). The denominator then becomes
    (cos t cos x + sin t sin x)²
    = (cos (x-t))²
    = cos²(x-t)
    This is the denominator. The numerator was 1.
    Therefore the integral becomes
    sec²(x-t) dx.
    Note that t is a constant. So, the answer becomes
    tan(x-t)
    Since tan t = 4/3, we can say that
    t = arctan(4/3)
    Therefore the final answer becomes
    tan (x - arctan(4/3))

  • @sokolo8
    @sokolo8 Před 3 lety +2

    51:01 this integral actually equals (1/12)*(6-sqrt(3)*Pi) . But at 51:55 the answer is Pi/4.

  • @PavlinMavrodiev
    @PavlinMavrodiev Před 4 lety +43

    The commentators really saved the thing. At least someone had to know how to integrate

  • @Exachad
    @Exachad Před 5 lety +1448

    As an MIT freshman watching the bee live: Wow, these kids are so quick and smart!
    As an MIT senior watching the bee: Lol, these kids take way too long lmao!
    In all seriousness though, the MIT Integration Bee is a tradition that must be preserved. Go Beavers!

    • @studywithjosh5109
      @studywithjosh5109 Před 5 lety +10

      Any tips for getting in?

    • @Exachad
      @Exachad Před 5 lety +187

      @@studywithjosh5109 Good SAT/ACT and SAT Subject test scores along with "decent grades" with a good choice of advanced subjects that match your degree. If you want to take Physics like me, take as many Advanced Math and Physics courses as you can. MIT is a very specialised school, so not taking too many humanities courses or "smart electives" (Electives that are academically oriented vs sports/P.E) like AP Seminar or shit like that, doesn't matter after a certain point. All the advisors at my school told the kids to take a diverse range of advanced courses. I didn't do that because my Freshman and Sophomore HS GPA wasn't good enough for MIT and so I said screw it, I'm going full Math, Science and English for my junior and senior year because French and Humanities were desyroying my GPA and that's how I made it. The trick is to take subjects you're good at and practice for the SAT. The SAT is incredibly simple in the concepts it tests. Nothing advanced, simple English and Grade 9 Math. Careless mistakes and bad time management are the enemies.

    • @revl6151
      @revl6151 Před 5 lety +81

      You're not in MIT with that stupid ass profile pic

    • @robbyburns5822
      @robbyburns5822 Před 5 lety +12

      @@revl6151 most people don't actively change the profile pic to that. A lot of those profile pictures are due from people hacking into youtube making people with that profile picture say "oh yeah yeah". obviously youtube debuggers were able to stop the waves of spam within a couple of days, but the profile pictures still remain because youtube isn't allowed to violate terms of user privacy (changing anyones profile picture)

    • @fbi8122
      @fbi8122 Před 5 lety +69

      Bob Jones what’s wrong with his profile pic

  • @themannyproject6653
    @themannyproject6653 Před 2 lety +2

    Why am I voluntarily watching something that had caused me so much pain

  • @pixelchu
    @pixelchu Před 2 lety +2

    Imagine studying for a final but watching this instead

  • @EthanBlaineMeyers
    @EthanBlaineMeyers Před 5 lety +21

    I'm about to graduate college with an economics degree and I haven't touched an integral since 2015. This is awesome content! Even the first round was fun to watch - much credit to the commentary booth.

  • @michael199316
    @michael199316 Před 4 lety +161

    I want a "where are they now" of this competition!

    • @benltownsend9014
      @benltownsend9014 Před 2 lety +39

      @UCJ2DFPYDjLvkcSvoMhN_YlQ I bet 1000 bucks they are 10 times more successful than you will ever be you absolute loser

    • @Repstar00
      @Repstar00 Před 2 lety +24

      @Macy sondheim yet here you are watching a 3 hour long video from 5 years ago of kids doing math in your free time

    • @___whateverr
      @___whateverr Před 2 lety +1

      @Macy sondheim someone just posted you i just came to witness this historical event

    • @lollel1490
      @lollel1490 Před 2 lety +4

      @Macy sondheim ngl you sound like a simp bro

    • @khair7549
      @khair7549 Před 2 lety

      Lol he got ratioed

  • @Trunxz
    @Trunxz Před 2 lety

    Woke up the next morning from falling asleep watching CZcams, and this is what pops up.

  • @maxwelljarman7785
    @maxwelljarman7785 Před 3 lety +5

    “That’s really sucky”
    Audience: 🤣🤣🤣

  • @user-ec5kh1iy8n
    @user-ec5kh1iy8n Před 3 lety +85

    2:31:31 So you're telling me mathematicians also have crazy fans who paint themselves and cheer for them in the crowd?