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.
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.
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 .
+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)
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.
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
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 :)
@@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)
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
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
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.
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.
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! =)
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!
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.
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.
@@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
@@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.
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!
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.
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!
@@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...
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?
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.
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.
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 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 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)
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
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
I'm a bit confused on whether David's answer was accepted. It was equivalent to the correct answer, but did they mark it wrong as he didn't substitute back?
You're not deaf, audio starts at 00:32
LOL i thought so
Thanks
no! ima bout to smash my headphone
Thanks
I scrolled down looking for that comment lol :")
Hahahaha thank u....
other colleges: at parties
MIT:
I went to Michigan Tech and we did this at our parties.
😂😂
wooooooo
theyre partying in their brain.
im down, beats sitting around wondering when you can go home without making your friends feel sad and lonely.
They really made some of the most traumatic experiences of my university career into a sport. They really built different.
idiot traumatised by maths
Her: he's probably out cheating on me
Me and the boys:
Lmfaoooo
This seems reasonable 😉
Lmaoooooooooo
"Hey, Keith, don't forget to upload the Integration Tournament to CZcams."
"Yeah sure, I won't forget."
*10 years later*
🤣🤣🤣🤣
🤣
He didn’t forget
But was he reminded?
Hahaha!
"I'm sure most of our viewers would be familiar with [insert mathematical concept here]"
Me: "Yes. Absolutely. Entirely."
For sure, no doubt, easy peasy...
😂😂😂😂
i got it.....😳
Yeah sure, except those cosh and sinh.
I’m surprised they didn’t know the first one
This is the most intently I've ever watched something where I can't even begin to comprehend what's happening.
Hahah, it's truly phenomenal.
Same
I woke up to this video playing and got so into it, i couldn't go back to sleep...🙆♂️
I love how the commentators make legit comments about integration. Absolutely amazing.
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.
NeverLooksAtComments he’s my dentist lol
@Phytom try an integral before you die, or you'll regret :haha
well yeah they said they wrote some of those integrals so obviously they knew what they were talking about
as a math nerd, differentiation was nice but integration was the cherry on the top
Edward Guterres what’s his name
17:24 "small mistakes crash rockets into planets"
I'm going to say that the next time my physics professor makes a mistake.
Tall Random Guy me too lol
I was about to comment this LOL 😂 that was hilarious
Tall Random Guy small mistakes cost lives and millions of dollars
hopefully everything is now calculated with a computer
And so he'll say when you fail your test 🤣🤣
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.
That's amazing.
What the fuck are you talking about
If I ever teach a class, I'm gonna steal that.
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 .
New roommate: So, what sports do you like to watch on TV?
Me: .. it's complicated.
The integration is pretty fantastic, but what amazing video quality for an amateur 2006 production!
+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)
@@KeithWinstein truly amazing..
its MIT, what do you expect ?
@@KeithWinstein 1:20:33 , pretty amazing for the time!
@@KeithWinstein While many teachers around the globe still struggle to plug a computer to a projector.
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.
How wonderful the world would be if everyone spent their time in such pursuits. Beautiful, happy, intelligent, wholesome people.
Was I looking for a 3hr video on integration? No
Did I watch it? Hell yeah
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
@Throngdorr Mighty ya so is integration
hell yeah thats the spirit!
@@alexandervu8693 the first hours was bad no one could solve their integrals, poor lads.
@Throngdorr Mighty ???
Did i really just watched 3 hours long integral bee instead of solving my homework on differention first
Nah don't worry differential are very doable,
james barns I feel this.
Watching this when I’m supposed to be working on series 😂
hahahah lol
no, you didnt
I have my Calc 2 final tomorrow
This one video has helped me be more eager to learn maths. I know it’s old, but I thank everybody involved.
commentator: "someone's gonna get this",
Li Yu and Ross: we can do this all day...
ha... what a bunch of nerds...
wish i could do that
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 :)
Prabal Baishya that is very true
Prabal Baishya I’ve learned that way, lol
And also through websites
It’s really about applying the rules
but can they fight or invite a girl out?
"They haven't been able to get the first 5 problems"
*Me on my 5 question Calc test*
MIT students: do integral the old fashion way
Me: google "integral calculator"
no cap haha
some of the extreme integrals couldn't even be solved by Symbolab or Mathway
Sometimes an integral will have multiple answers all correct
@@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)
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..."
Sarcastic
The commentators are fucking great. The way they explain what the guys are doing, what method, what it means. wow. this is actually interesting
Aren't they amazing?
@@amyfalconer1660 truly amazing!!!
What are their names?
When the Athletics Dept is involved with the integration bee, you know it's a tech school.
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
"this is Sport Cast at MIT." 5:18 im wheezing
Now I know why I wasn't accepted at MIT
Danilo Correia yes judging by your sentence we can all tell why you were rejected from mit
@@Junzipark8881 shut up kid
@@Junzipark8881 Cause he misused the preposition "on"? Kind of ironic considering in your sentence "by" would be more appropriate than "from".
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
harsh tripathi alright man it was a joke in the first place because he probably did not apply to mit in the first place
imagine if there was a professional league for this.....
there are people who could integrate these in their head in two seconds
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.
51:02
The world world would be a better place
@@jmika5984 That integration was really simple and easy
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.
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! =)
Indian high school students writing the entrance for the IITs are way more intelligent than them.
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
Some of these were soo easy 👍
@@DeadPool-nx3gyGood for you my guy
The dude with no shirt on showed up at the wrong party
No he was great
"Not a bad crowd here tonight, gotta be at least 60-70"
*Laughs in 619,000 views in 2019*
1,000,000 mark 2020
I read that as 60-70 inches
@@bovino9245 1.3 million views on October 22nd
1,487,501 views Dec 5, 2020
1500000 views 2021 6th january
It’s crazy that when I first saw this, this was some crazy math shit but now i actually understand it all
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!
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.
This is the only good MIT integration bee video I can find. Any other years' videos as high quality as this?
I would rather watch these than sports any day
Can’t believe this was made in 2006, Windows XP era
Yeah these guys should really consider going into a field with technology in it considering how good this video is
2006 was not the 1960s either
These are the people your math problem tells you not to worry about.
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
bruh
This is honestly such a genius idea. Its an easy way to get your students extremely comfortable with integration for the higher level courses.
Somewhere in that crowd, someone is solving all these in his/her head.
but that someone wasnt able to clear the test to be selected for this event
Utsav kataria or didn t try
no there isn't. Integration isnt like that.
His name is Will Hunting
@@nukemars9445 I find it highly unlikely Nikola Tesla is sitting in that crowd considering he died over 70 years ago...
I can't believe I watch all three hours of this without getting bored. HAHAHA
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.
How do u get an A in calc 2 and not know what cosh is lol
@@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
Do the students down the hall in the MIT laser lab have a disintegration bee?
differentiation is too easy to have a competition, I guess.
Kushal Bastakoti chutiye
I chortled
No diffeqs? There would be some fun ones there lol.
@YouBuet Trust me, a woooosh ain't needed around here :p
Differentiation is definitely easier than solving integrals
The thing I loved the most is that the commentators know what they are talking about...they seem to be MIT integration bee veterans
Definitely Intergral
@@Lk_boca lmao
The commentary really made this thing what it is. Surprisingly I watched through it all and quite enjoyed it lol
There's something cathartic about watching MIT students make simple math errors
They're definitely trolling us by calling these "trivial" or "easy" integrals.
No they are actually easy.
they are easy...
Trivial means classic
They arent too hard, but they require tricks
Um yes they are actually
Very few hold the title of “Grand Integrator” at MIT and this legend is one of them
I won in 2013 lmao
@@deathzone4046 wow respect
Are you Justin brereton
@@RandomPerson-iw3mw yep
@@deathzone4046 Well, you are a nerdddd
@@deathzone4046 what are you doing now out of interest
As a mathematician myself, I enjoyed this video and frankly speaking, I learned some stuff from it as well...
it’s literally 3 AM and i woke up to this what?
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??
@@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
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!
Thanks so much!!
@@nl7837 no problem!
+
F
can we talk about how the rewards were VERY underwhelming
gotta love the dude with the double integral face paint
I really fell a sleep watching CZcams and woke up in the morning to this😂
I have a geopolitics paper due next week, this research is quite helpful!
I felt bad that I couldnt solve these, but then flet better when they couldn't either
those were pretty easy , wonder were they mit graduates or not
@@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.
@@EDROCKSWOO they are nerds anxiety comes with high intelligence
@@mridulbhatt8917 Anxiety comes with high intelligence?
@@bee_irl It's not proven but a lot of "geniuses" tend to have anxiety in some sort of capacity.
1:18:47 the guy on the right is my situation
Lmao
So true!!!😂😂
Ee
1:19:12 LMAO
Also me.
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!
Somehow I watched about an hour of this without realizing it and I have no memory of it.
I never thought I would hear the word "extreme" next to "integral"
Pretty much every integral is 'extreme' to me lmao. That's why I solve my integrals numerically
The commentator is the real mvp/math wiz during the finals.
yeah, guess mit profs are like that...
The commentator is the camera guy in this video: czcams.com/video/9y7L8kAuPxs/video.html
@@athena546 was mmm
D I itI’ts YI eah that’s @@athena546 ir I’m okay good good job buddy hope hope you’re ok
Dfddffffffdfffffff
I fell asleep with my phone on and this was in my history 💀💀💀
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.
3:00 AM Always leads me to weirdest place.
at 3 😂😂😂lmao
2:28 for me lol I'm close
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.
im a sophomore in HS taking geometry, i love having my mind just melt watching these
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
bro go to sleep man you've been on youtube too long
aite fam you're right gn
Nah it’s only 1am
Fam you are right
its 102 Am rn lmao
2:49 here, you’re right, good night!
3:48 dudes got binoculars lmao
Hes cute
hes not missing anything 🤣
@@beamerz9398 😂
the commentator made calculus interesting for 3 hours straight someone give this guy a nobel
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!
2:51:20
Interesting battle going on I wonder who is going to wi....
Cameraman: nah fam look what these guys are up to
Underrated
Lmao
I'M DEADDDDDD
Wtff
Kiss it and miss it.
Me: notoriously sucking at maths since 5th grade
CZcams: yeah let's recommend this guy integration bee video from MIT
Why am I voluntarily watching something that had caused me so much pain
?
@@dyhsehehb6232 I fucking hate calculus but I found this video really interesting
The commentary kept me interested even though this is above my skill level. Happy I stumbled on this video. Learning is always exciting.
There MUST be a competitive league for this (Or maths). The casting makes this SO SICK
There is lots of maths competitions. Not live events though.
@@MrCmon113 would've been cool if they were live broadcasted like this with a comentator
@@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...
there is. it is called mathcounts countdown national competition
@@user-vo8zx1db6m this was, but his point was that usual math competitions would not be.
44:57 *"Hard to see how that would be zero"*
savage commentator
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?
@@ninetales1234 but sine is always positive lol
@@deadlypyre act of desperation
How Fascinating This Is😩💗
Imagine studying for a final but watching this instead
I cannot believe I watched the whole thing. Oh my gosh. Kudos to the commentators who kept it engaging.
This needs to be on ESPN. Where's the 2007 season?
Even though I haven't learned integral, watching this is pretty fun
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.
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.
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!
Any tips for getting in?
@@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.
You're not in MIT with that stupid ass profile pic
@@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)
Bob Jones what’s wrong with his profile pic
ESPN: The Square Root of Ocho.
I would prefer the cubed root. No surds please! :P
There’s an ESPN 2.82842712?
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
Commentator has to be some kind of a PHD student
Really knows his stuff while still being more entertaining than a professor
2:13:28 *confusion intensifies*
"high definition" is an understatement considering this was 2006
i fell asleep and i woke up 2.5 hours into this... whaaat.
Now all these geniuses are programming algorithm through which I am seeing their video 15 years later.
It would be fun to see the faculty version of this. Special functions, grassmann variables, path integrals...
Haha, yeah... I know, right? They would totally do those things you said, as we all know.
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
The commentators really saved the thing. At least someone had to know how to integrate
2:24:06 damn that circling battle was intense
This is so much more exciting than sports! The suspense!
F
I'm a bit confused on whether David's answer was accepted. It was equivalent to the correct answer, but did they mark it wrong as he didn't substitute back?
Left autoplay on on my pc and woke up to this
Great Commentary.
@@edwardguterres8964 dentist knows integration?
“ i think everyone wants to see a right answer at this point “ - savage
I would have left my career at that comment !
No idea why this was recommended to me. But thank you to all the competitors 10 years on. The fries you served today were fantastic.
Man this is by far the absolute most confusing thing I've woke up to
This makes me want to improve at mathematics.
Hydroxoid xqcL