Omg Yan you are amazing!
I would have totally watched this over the superbowl!

an excellent adventure,sport.

omg that's some rapid repeated integration jeez.

i actually feel kind of relieved that i managed to integrate half of the integrals yan posted above.

Wow...
Just wow...

On a side note, watching the Integration Bee after the Superbowl, I think I enjoyed the former more.

But then again, that might just be because I live in Tucson (AZ) and the Superbowl was spoiled by the defeat of the Cardinals and other shenanigans... (thankfully, I was watching in high def)

Haha you can see the guy's chalk actually vaporizing off the board when he speeds to circle his answer! :-)

Aaah! Integration bee - definitely not for me!

AHAHAHA Kevin, that must have been great. I heard what "flashed" on the screen in Tuscon. Someone even uploaded it, so I could watch it in all its glory.

Any chance at a derivative bee? haha, i might show this to my calc class for kicks :P
-Jamo

Or not to Integration Bee, that is the question. Actually, that's not the question. The question was an integral.

Guy in Red Shirt == Brayden Ware'11, UMA Publicity Chair'

The Grand Intergrator == Murtaza Nek'09 (who also won two years ago!)

I remember having to integrate cosh^-1(x)dx in a DiffEQ class I took last year. Can't remember how though.

Can't cos^-1(sin(x)) be rewritten with square roots thus making it easier?

And cos(3x)/cosx you just cancel out the cos and the x to get the integral of 3 dx. Duh.

Anyway, derivatives are math. Integrals are an art form. This is proof.

yo nur, i think

guy in red shirt == Dave Reens '11, the godliest math beast ever

WAITAMINUTE.

That integral that you posted the video of in facebook (and here) was the LAST ONE in the competition?!

But that was... that was easier than almost any of the qualifiers! It was the only one I can honestly say I would speed-integrate with zero issue!!

Well, after reading some of the other ones you posted pics of, I can honestly say that a couple throughout the competition were easier. But still.... Maybe I just haven't learned enough methods yet, and it's a coincidence that I knew how to do the last one? Or was it really that easy?

Yeah, Murtaza won! ^^

In response to "hey nur":
No, Dave Reens was wearing a ZBT t-shirt( I believe it was green?). I was one of the judges at the bee and I distinctly recall Brayden being called out because his answer was aesthetically displeasing along with being wrong. ^_^

Err... Ilya... uhh... no offense, but since it would appear that you were serious throughout MOST of that post, I must ask what you were smoking when you solved "And cos(3x)/cosx you just cancel out the cos and the x to get the integral of 3 dx." Since I'm exhausted, I probably did something wrong in the following, but I believe it should be
cos3x
=cosxcos2x-sinxsin2x
=cos^3x-cosxsin^2x -sinx(2cosxsinx),
so you take the integral of
(cos^2x-sin^2x-2sin^2x)dx (after dividing by cosx)
=integral(cos^2x-3sin^2x)dx
since it's from 0 to pi.... that's....
pi/2-3*pi/2
=-pi ??
Please correct where I made a misstep (I'm actually assuming I did, since I'm tired, rofl) and I'll see it in the morning.

(and for the record, Ilya, I know you must have been joking, but since you were serious through the rest of your post and had that blatant ridiculousness added, I felt the need to find the integral for myself)

Graagh, I hate me for forgetting triple angle formulas from trig.

forget that crap above, it's integral(4cos^2x -3) from 0 to pi.

Though that means I still got the answer right... thank god.

lol don't buy biology text books. BORROW THEM.

also, i don't think I can do a single one of those integrals

@Narce
didn't know there were triple angle formulas, although I guess they're not hard to derive. I just did it the same way you did it the first time.

I just might have to try out for this if I get in. I wonder if any other schools do this. I found I could actually do most of the ones you posted and on the qualifier (which was good for my self-esteem), just not nearly quick enough.

Have you ever noticed that the way a person draws the integral sign tells a lot about his personality?

speaking of calculators, I find it a bit amusing that the algebra system on my TI-89 actually can't handle some of these

Well yeah, most of them can be done easily and quickly but it all depends on how accurate you are given the required speed. I guess it's the combination of those 2 that makes it tough - my school chemistry sir told us that he'd discovered an analogy to the uncertainity principle - speed and accuracy!

@Ilya - try to make a distinction between when you're joking and being serious. For a minute I actually thought you were serious about 3dx!

NATURAL LOG CABIN.
Hahahha, after our Calculus student teacher showed that to our class... I doubt I'll ever get over it.

aahhhhh, but you didn't learn the whole thing,

The actual answer is houseboat- (natural log cabin + C)

Holy --- wow, I've actually seen a couple of those in my calc class. And I'm still in high school.

I KNEW IT - my school's class IS abnormally hard! I feel so much better about being so awful at it now. :D

LOGe|CABIN|

What's the modulus of CABIN?

+C, of course. :D

@anon, a couple of those were actually quite basic, as I've seen them before as well. There are very few from both this competition and the qualifier test (found easily from a google search) that I found unsolvable (for me... so far), but I'm in the same boat as Matt: I can't do them quickly enough, except for maybe 5 total throughout all problems that I can do in under a minute each.

I said @anon, but I meant @Anonymous (the last one). I hate how people will actually type in different ones -.-"

@Narce @Varun

Haha I figured people would recognize that someone who knew what cosh^-1 was would know that cos(3x)/cosx != 3, but I guess I should watch my verbal irony. :P

That was awesome! I did enjoy the Superbowl, but having a husband from Pittsburgh makes that a marital requirement.

Since I have taken on the name MIT Mommy, I felt it appropriate to introduce myself to more MIT Bloggers.

Right now I am not worried about these integrals that I cannot solve but I fill with immense pleasure on the thought that someday in a tough Math's class at MIT I will learn these new and fascinating things.

Drawing houses during a face-off. Best temporary childhood yet. I haven't had a childhood since then.

Guy in Red Shirt is Brayden Ware.

@Teddy

You're my best temporary hero yet, btw.

the other guy in the video is Murtaza Nek

After I brush up on my integration, I would def watch this over Superbowl! bbuuhaahahha. That's going to be a hard choice for those who loves math and superbowl to pick which events to watch. :p

O MY GOD this looks so fun and amazing

But he never put plus C... lol

Thanks to Nur and everyone else who commented on the names. It's been inserted.

Tricky integrals have always bothered me, if only because they're one of those things where the answer/method is always so simple once you actually see it.

I'm surprised actually. A few of those integrals would be something I would expect the average MIT integration enthusiast to memorize before going on stage to compete. Certainly cosh-1x and the decomposition of cscnx. Is there a differential equation-solving competition?

hmm.. html superscript does not work. That's cosh^-1(x) and csc^n(x)

Oh my. I didn't know that one could be so competitive at Calculus!

My thoughts while reading this entry:
Oh my god I have to go to this school.

Thanks, Yan

When I read the title I thought you were talking about the PETA ad.

Man, this pwns!!!!!!! :D
I'm game for it.

I love it! I so wanna come and participate in this, even though I might be out after the 1st or even 2nd round, it looks so fun! I would def. watch the this over the Super bowl!

unlike many others here, I am actually quite intimidated by this bee.

the integrals scare me; the calc scares me. I wish I could feel the math love that everyone else seems to, but I feel like I wouldn't belong even if I got in by some fluke.

oh dear, oh dear. xD;;

though I must admit, it looks more entertaining than the superbowl.

@ Stephanie:

Honestly, most of MIT couldn't do these integrals. Remember, only a handful of students actually make it to the finals of Integration Bee. The rest of us sit at home and play with Mathematica.

This is the coolest thing ever.. as good as HMMT's Calculus Test!

Wait, MOST, Yan?! Of MIT?!

Tell me the lowest score that made it past the qualifier, if you know it, please. Because pure mathematics is my #1 specialty, even though I prefer comp sci and physics, and I really don't want to sound arrogant, but I genuinely think I should be able to get past the qualifying round after re-taking calculus at MIT.

http://www-math.mit.edu/~tkemp/integrationbee/

This site should suffice. In bed.

Well, that's already how I knew what the qualifiers looked like, since a google search gets ya there ^.^ Some of the things I couldn't remember the methods for, and a couple I just plain never learned yet, but I've already mentioned that XD

But Teddy, did they tell you how many qualifier problems you got right? Because you were 4th out of those~

Whoops, the above was me.

To clarify:

Most of MIT couldn't do these integrals in the time allowed (4 minutes each).

Actually, it's fairly certain that most of MIT couldn't integrate cosh^-1(x) anyway.

Remember, not everyone here even likes math.

Luckily, being able to solve tricky integrals is not a requirement for being brilliant/innovative/great at designing stuff.

Hey,
I got a score of 108 out of 120 in Toefl(ibt).Is it good enough for getting admitted as a transfer student in MIT?

I have to ask, did anyone get that 4/(4+sqrt(4-x^2)) one on the spot, it looked simple, but it wasn't, and it bothered me until I found the solution which I actually had to find an online integrator to give me the answers to various steps and work backward to get.

Ohhh, it makes sense if you add "in the time allotted" XD Err, well, I can understand students not being able to derive the integral cosh^-1, but to be perfectly honest, I would just memorize the more obscure integrals before the competition. Like that one.

And while of course not EVERYONE at MIT likes math, I should hope that more than half do, even if they like their science of choice more. MIT isn't the best place to go for a huge number of people who don't care for math, I'd say ~.~

Lincoln knew calculus!

@ Narce
You can find the 2009 qualifying test and solutions here . These 20 integrals in 15 minutes, admittedly, is pretty insane. It took me six minutes to get the first three.

And, a derivative bee would be way too easy, because those are almost always doable.

I've mentioned like 3 times in this comment section that I've already looked at the qualifier! If you're going to direct someone to it, at least don't direct me!!

That was a great entry!
And you actually made math more fun than it is :D
Kudos!

"For now, I will be a non-lame blogger and give you a lot of hard integrals. Last Wednesday beheld the night of MIT's annual Integration Bee, the spelling bee that only uses about a third of the letters in the alphabet (x, u, c, o, s, i, n, h, e, l). "

Actually, you missed 'd' ;) :P

ln |CABIN|

! I like it.

"MIT's math fanatics (aka, the rest of MIT)"

I also like that.

This is straight up crazy. I doubt I've met to an MIT student yet who could do even one of those integrals. my goodness.