MIT Integration Bee Final Round

[albertx2]

what is integration

[thementor8]

hhhhhhhhhhhhhh u call this a prob

[haytnas]

of course it had to be the terrorist that won.

[MultiBrados]

Painfully easy integral to calculate.

[urdouchbag]

im sure the guy who won had done the same problem before..... 

[darnit78]

I LOLED HARD AT THE ASIAN GUYS DRAWING OF THE INTEGRAL XD! TOO FUNNY MAN! LOOKS LIKE A RANDOM LINE XDDD

[Matthew2400]

That took me about 3 minutes to solve, these guys did it in about 30 seconds :O

[fredboy6]

awsome solution! he only added 0's to simplify is equation didn't even had to work hard for that one but thinking to use that path is AWSOME!

[urdouchbag]

LOL...no American in the final round??

one is Asian ..other is Middle Eastern....

[feuchster]

@urdouchbag What does it matter if native american's weren't in the final round...?

Though, I probably know what your confusion is, you are confusion anyone that isn't of the skin color 'white' to be non-american's. See now, that's just crazily absurd.

[urdouchbag]

@feuchster lol where's skin colour in my comment?....both have American skin colour...but what you probably didn't see was the big ass beard that's there in his face which is clearly not a style statement...and other guy is Asian read comments below. ''I LOLED AT THE ASIAN GUYS DRAWING OF INTEGRAL.

[feuchster]

@urdouchbag Nope, I have american friends with beards that have ancestors from the middle east. They were still born in america; therefore, they are american's

[Cammie010]

LOL..integration bee?

[MrBigEnchilada]

so im guessing he used long division in his head and just got the result into the answer based on memorization (as anything of the form S 1/x dx = lnx)

[hongwei1234]

all american

[warwize]

you could use inverse hyperbolic tan but his way is easier

[iickle]

Oh, fuck all you pretentious armchair geniuses. Can't you pricks just watch the damn video instead of stroking your egos? 

[bushidodude]

Long Division and a purely computational exercise, but damnit I love MIT chalk!!!

[semmeias]

Damn, I took 20 minutes to calculate it.

But wait... the guy left out the "+ c" !!!

[JLyau]

@semmeias it is not necessary to

include the arbitrary constant C in bee

[khanshamim1]

i appreciate that he did a nice job but in the middle of 1 of the LN should be + not -. but everything else way fine.

[SevenRiderAirForce]

where's the wise ass who does it in his head?

[Arihanta1112]

Interesting.

[PurestLogic]

wtf fail, a simple "sin" substitution would have taken much less time

[tryceo]

@PurestLogic It wasn't under the sqrt... so you can't use inverse sin

[PurestLogic]

@tryceo No, I'm talking about trigonometric substitution, letting x = sin(theta) and dx = cos(theta)d(theta). This substitution would have been easiest.

[Meanman332]

@PurestLogic No, I think it would have taken longer. 10 seconds to write out the substitution, then you have to deal with sin^4(theta) over cos(theta). Change that to (1 - cos^2(theta)^2 over cos(theta), expand that, integrate the easy bits, then deal with the cos^3(theta) term by changing it to cos(theta)(1 - sin^2(theta)). Would have taken about 10 seconds longer by my estimation.

This was a ridiculously easy integral though. Surprised this was in an 'integral bee'.

[vibins360]

Haters gonna hate!!!

[lamestguyintown]

is MIT supposed to be a good university? i did these sort of equation for my gcse..

[mrdbzfann]

Really no offence but we do way harder problems just for AIEEE or IITJEE examinations

[godling2007]

@mrdbzfann doesn't matter. Academic difficulty of university courses does not determine the quality of life you will live or how much you will innovate going forward. The US teen population compared to the Indian Teen population speaks for that, right?

[joejacksonriley]

no credit. He forgot +C

[bmx391xmb]

that was a disappointing integral.

[kldaace]

He forgot +C!

[improlawl]

wheres the +c? ... O.o

[VanMedia]

this is basically a battle of who can write faster lol

[AlmightyInsanity]

0:01 *Yawn* after seeing the question 

[lawnmowingjob]

He forgot to put a "+c"!

[Ragib]

Note to all: In most integration bee's writing the additive constant of integration isn't required, as it is assumed to be obvious by that level.

[Zoidypoo89]

Could someone who's good at math explain how you'd integrate something like that?

[Ragib]

@Zoidypoo89

Subtract and add one into the numerator so it becomes: (x^4-1 +1)/(1-x^2)

Split the fraction into two: (x^4-1)/(1-x^2) + 1/(1-x^2)

For the first fraction, use difference of two squares, so its numerator is x^4-1 = (x^2-1)(x^2+1), so the first factor cancels with the denominator, and just: -(x^2+1) is left, which integrates simply, so the first fraction is done.

For the second fraction: 1/(1-x^2) = 1/[(1-x)(1+x)] = 1/2 [ 1/(x+1) - 1/(x-1) ], which are simple to integrate too.

[Zoidypoo89]

@Ragib Damn. I didn't expect it to be THAT easy. I actually feel kind of dumb that I didn't figure it out myself. I don't usually have to integrate anything "weird" at all in my multivariable calculus class though, so I guess I haven't had any practice at it at all. But still, I'm kind of amazed that it wasn't any harder than that

[theoriginalwasa]

woah... that guy on the right was a total loser... I had the answer in my HEAD before he worked out he didn't even know how to do it.

[Yu2Kal]

@theoriginalwasa Ok you arrogant fuck, if your so good why don't you try something more challenging, like maybe getting a life?

[theoriginalwasa]

@Yu2Kal Hey... Speaking of getting a life... Im not the one at an INTEGRATION BEE for rookies... Don't be hatin' man. Also, look at the other comments (like the top rated one), Im clearly not the only person that thinks this.

[bezaldo7]

The first round was probably integral of a constant.

[yitzchak13]

FAIL

he forgot + constant

[zx6rtt]

legend has it

that if you cut off his beard, he looses his integrating powers

o_O

[ericmoss13]

Here we have the two extrema of quality of integral signs.

[mozam007]

dont u need to add constant?

[TenTonNuke]

12 years of grade school perfection. 2 years of junior high stress and studying. 4 years of high school social sacrifice and discipline. Get accepted and pay hundreds of thousands of dollars in tuition fees...

...and you get to watch a middle eastern guy and an asian guy math battle for a hat.

[snoktruix]

Looks like the winner actually got the sign of the x^3 term wrong.

[gremlinextreme101]

@Oxydox Not at all, it is required for the general solution. Otherwise you end up like Bernoulli and believe that ln(-x) = ln(x), a mistake that was made because he failed to realize the importance of +c

[99ludester]

@Oxydox Not in my university...we better have all the correct notations for everything in the math department. This includes all of the "dx" on every step up until the integral is taken and "+c" after the integral is taken. Same thing with limit notations, etc...In the physics and engineering departments we can get away with these technicalities, but they have other ones in which they are extremely picky about.

[MICHAELMEMISBACL]

Math's not meant to be a game;

[arioscos]

Wow. That was it? Even I could of solved this problem in seconds. Partial Fractions ofcourse.

[sjsawyer]

Where the hell is your arbitrary constant son!?!?

[cdbongo]

Pretty impressive - I wish my school had this!

I bet the guy on the right would have won if they were required to show work; he really had the simplest method with the separation thing he was doing. However, all that matters here is the quickest answer and I have a feeling the guy on the left had that last fraction memorized.

Once you do enough of these it's all about how quickly you can reduce it to a memorized form.

I bet these guys can do some sweet partial fraction tricks in their head

[trese0000]

Did anyone think that was fast or what? I still can't figure out what they did with the expansion of some sort of the numerator on the very first line. I am not getting the natural logs that he is getting. I got: -1/3 * x^(3) - x - inverse cotangent of x + C.

I used polynomial long division and came up with: - x^(2) - 1 - 1 / (x^(2)+1).. Anyone no a mistake I made. Thanks

[SniperMaske]

@trese0000 I personally find -x²-1+1/(1-x²) (which is consistent with the student's result since 1/(1-x²)=(1/2)/(1-x)+(1/2)/(1+­x)), so I guess you got tangled up about a minus sign somewhere.

One way to see it: x^4=(x^4-x²)+(x²-1)+1=[-x²-1+1­/(1-x²)](1-x²).

[sid9221]

Tht was pretty easy.... not what i would expect from a MIT integration bee.

[KamuiX707]

I thought when you box your answer you couldn't edit it further. I guess the rules are a bit flexible here.

[KujaRhapsodos]

What the...? What are those challenges? And aren't they supposed to be hard?

[thevidfather]

Holy CRAP that was fast!

[mathswithinsaf]

nice!!!

[partonfilaton]

xa00ax0ax0a0ax0  integration bee hillarious

[Ragib]

Thats totally pathetic for the final round of a MIT bee. That integral takes 10 seconds max.

[oddzonezout]

lolnoob

[mkeeeee]

@Ragib Higher mathematics talent and general scientific intelligence does not imply quick integration ability.

[Ragib]

@mkeeeee No there is no implication, but there is correlation. For example, mathematical talent doesn't imply knowing many digits of Pi, but you would notice the average MIT math student would know more digits of Pi than other groups.

[Kadozier]

@Ragib

nerd

[BallawdeQuincewold]

@Ragib You fucking idiot. There's a time limit.

[Jef11235]

@BallawdeQuincewold Yea i realize theres a time limit. What makes you think I didn't know that?

[MrBigEnchilada]

@Ragib liar you cant even write it out in 10 seconds besides you would need to memorize the formula to do that

[MICHAELMEMISBACL]

If this bee were for a grade, I would say deduct points for forgetting the +C ! One point off for forgetting +C; that is the fairest penalty ;).

[abaddon1112]

major points.. seriously.. I learned that shit real quick in class hahaha

[MiketheViking90]

the +c is usually omitted for most courses past AP calc

[Wampa181st]

very important once u have things with U(t)Y=possibly only C

C almost always important just in case

[moreoriginalusername]

I really hope that the +C isn't required for the integral, unless I totally missed it.

[MICHAELMEMISBACL]

If you are dealing with a indefinite integral, you should put +C at the end; teachers reserve the right to take points off unless they are forgiving. With definite integrals, which have a upper bound and lower bound, you do not need to show the C.

[MICHAELMEMISBACL]

I had a teacher that would deduct points if +C was forgotten for an indefinite integral, if I remember her correctly.

[MICHAELMEMISBACL]

How did that guy on the left get 1/(1-x) and 1/(1+X)? Adding those together yields 2/(1 -x^2), not 1/(1-x^2) which is what I got when I did the division. Did the instructor make a mistake?

[MICHAELMEMISBACL]

We had a good teacher for Calculus II; we could use index cards with formulas for the tests.

[NickFL9ps2]

Calculus, Oh Calculus! Get a good grade in Calculus!

[MICHAELMEMISBACL]

Don't reply to me again.

[MICHAELMEMISBACL]

I mean it, you user of NickFL9ps2.

[MICHAELMEMISBACL]

Nick is not a math major; I am.

[NickFL9ps2]

Why did MICHAELMEMISBACL get thumbed down for mentioning that he had a Calculus II class with a teacher whose policy was that the students could use index cards for the tests?

[taledarkside]

@NickFL9ps2

either someone felt thats pretty much cheating

or you didn't really understand the concepts of calc 2 by not having to remember proofs.

[MICHAELMEMISBACL]

Use polynomial division, integrate the first terms of the quotient, and use partial fractions to solve the last term unless you have a formula written down for it.

[montyalbo]

I find it creepy that I understand everything they just did.

[drpwn]

I could do it faster.

[Webstedge]

the dude on the right was my 18.02 ta I think

[okman1234567]

THATS COOL