5 Challenging Integrals from the MIT Integration Bee

The MIT Integration Bee is one of the oldest and most sacred traditions at one of the top STEM institutions in the world. Today, we try to tackle 5 of the most challenging problems from the 2006 MIT Integration Bee. I hope you enjoy!
Here's the link to the original video, as promised: • MIT 2006 Integration Bee

[@istvanszabo5745]

Let's graph f(x). As you can see, its just a triangle. Yeah, of course i see :D

[@SISKCERTWaJaVlogs]

the triangles color is orange. thanks for your enlighted controbution to the cause

[@liamturman]

I loved this video, amazing animation and easy to follow.

[@pranaviyer8178]

Great video! Keep it coming!

[@GlowingMpd]

Don’t get dumbing this down by putting completely unnecessary and distracting music over the narration. 👎🤷🏼‍♀️

[@The_Shrike]

Well explained

[@abcdefgq1816]

Stupid question : where do the bounds of the integrals come from ? They don't appear until you solve those integrals in the end...

[@FaranAiki]

They forgot to write it.

[@ernestschoenmakers8181]

You didn't show the steps at the last integral where integration by parts was performed.

[@Deupey445]

The resulting integral from the first integration by parts is the opposite of the other integral

[@nadiyayasmeen3928]

The third one was nice

[@megaming1137]

Third one is an indefinite integral

[@rosgori]

He forgot the limits of integration

[@asharaghav719]

These are question form NCERT in 12th class for Indian people these are nothing compared to jee advanced questions 😂... btw nice video 👍♥️

[@ES-qe1nh]

Yeah india might want to figure out how to stay innovative instead of making ludicrously difficult exams

[@amartyasarker2077]

just see the mit integration bee, those guys don't even know the equation of sin(a - b) + sin(a + b) they just proof it a 3min integration bee problem, those indian guys memorize them at the age of 0

[@dhruw9935]

Its a test of speed bro even u and they cant do it so fast. just calm your butt down.

[@maalikserebryakov]

build a toilet? *indians sleep* do integrals? *indians awake*

[@syed3344]

no def no,last problem was a jee advanced level question

[@josealberto3108]

For integral 2 you can also do the substitution x = pi/2 -u, it becomes 1 +cosu = 2(cos(u/2))^2 Then we have integral of secant squared which is doable since its equal to tangent

[@isaacmalik3714]

im in year 9 and i watched this whole thing having no clue what was going on but it looked cool

[@itsshahain5954]

Just use t = tan(x/2) for the second question. For the 3rd question Integrating by parts is so easy, you get (x)(arcsin(cosx)) + (x^2)/2 + C. Anyways nice video!

[@ガアラ-h3h]

Even easier way found do it this way my friend I = int arcsin(u) * 1/sqrt(1-u^2) du => arcsin^2(u)-I +c => arcsin^2(u)/2 + c

[@atharvasawant7]

Indian board contain same type of questions

[@deepashsati79]

In 2nd question u can write sinx/cos^2x to tanxsecx with Is integration of secx 👍 Do not let u = cosx 👎

[@aminejadyani5651]

For the 2nd question, where did the bounds of integration come from ?? They werent there in the 1st place

[@maalikserebryakov]

He pulled them from his ass :)

[@wryanihad]

The last one is beutiful

[@acscp125]

Wait how is the first one challenging.....

[@recepduzenli3263]

Böyle matematik mi çözülür.slayt gösterisi gibi.cografya dersi mi bu.hangi işlemi yaptığınız belli değil.sacma sapan bi slayt gösterisi olmuş

[@markadams2979]

Animations are superb!

[@thephysicistcuber175]

You said you watched several of those, which ones are available? And links? (I've watched the 2015 one)

[@Salmanul_]

Nice animations, really enjoyed the video

[@leonard6355]

Which software do you use for animating the algebra operations?

[@Joshua123456791Funny6791]

He uses manim: github.com/3b1b/manim It's a python library created by 3blue1brown. It's absolutely amazing!

[@ansonlee3714]

I’d love to see more maths / science videos!

[@Yuuki3uwu]

3:13, how about just write sinx/cos^2x as tanxsecx, and then integrate tanxsecx= secx? I’m sure that is faster than u substitution right?

[@joaquingutierrez3072]

Yes

[@FaranAiki]

Yeah, but this is _easier_ (and the derivation of tan(x)sec(x) is calculated, no formula).

[@ahmedkamel5340]

for the second question we dont need to substitute we can just do sinx/ cos^2x = sec x . tan x and then integrate so the answer will be sec x which is the same as 1/ cos x

[@mohammadalkousa2856]

Great! Recently it was published a book about MIT integration bee, under the title " MIT Integration Bee, Solutions of Qualifying Tests from 2010 to 2023" You can simply find it!

[@shiksha6056]

As a normal Indian student in class 12 It seems easy and I was able to solve all these

[@thesecondderivative8967]

7:00 I think the integral becomes faster if you let u be sin 100x and v be sin^100 x. It follows that the integrand is just the derivative of uv divided by 100 and by fundamental theorem of calculus, the answer is easy to see. How would you know to do that? Pattern recognition. Also, I've noticed that sums on the bee tend to be derivatives of products in disguise. The real ingenious part is understanding that you need to split the sin(100x) into a sum.

[@benhardy6167]

greeat vid

[@tryingtopredict134]

Being a JEE aspirant, I was able to solve four of them with my syllabus .......... So is JEE difficult or is MIT's integration bee consists easy question ??????

[@qedmath1729]

I am in 9th grade from the U.S and I have seen some JEE integration problems. I would say they are not too tough because you only need to know a couple of tricks. Such as the "kings rule" and the fact that that the differentiation of denominator is in some form of the numerator. I am not posting to "show off" but rather to give what I think.

[@tryingtopredict134]

@@qedmath1729 hmm.......ya. But I hope you would have checked out some jee advance problems and you can't judge the complete set with some sort of problems. It maybe true that the problems you picked up requires basic calculus and just short of tricks but I guess their are enough variation JEE advance can present you with.

[@qedmath1729]

@@tryingtopredict134 Yes you are correct, most of the problems I saw were from the JEE mains test, probably the JEE advanced problems are way harder.

[@minh2901]

JEE is just a couple of problems using obscure tricks to solve. There is nothing special about JEE. You Indians just have delusion of grandeur.

[@minh2901]

As the result, after JEE, all IIT or other universities in India are a joke. They cannot produce research mathematicians, only broken robots doing non-creative, repetitive work. And when you bring this up, they bring up Ramanujan. Well, Rama is an outlier, not a representative. And Rama is educated at Cambridge, not India. In the end, JEE is just a joke that gives the students a false sense of superior. If india has so many people that are good at maths, why don't they have lots of Field medalists? Why field medalists seem to come a lot from Europe and USA? See ? if you can only do obscure elementary maths, all you do is to complete a hoop people give to you, not contributing to real research.