Now that it's April 2nd, I can finally explain that THIS IS NOT FROM MIT INTEGRATION BEE!!! As a problem writer myself, PLEASE DO NOT ACTUALLY LEAK REAL PROBLEMS! That is cruel and the amount of work into problem writing just goes into waste. So please, I do not encourage leaking competition problems. The following set of problems in this video are mock problems for people to practice, learn, and prepare for MIT level integration bees. In this case, this video showcases MIT Integration Bee Training Mock Problems. I will say, I made this problem bank way too accurate and realistic, so I don't blame others for reporting posts from different sites. In fact, huge props to the math olympiad communities for taking any leaked problems down as fast as they can. I technically deserved that temporary lock from AoPS to be honest xD Thank you everyone and I hope these problems help practice for olympiad level integration bees!
25:58 Take the tyalor series of ln and cancel out terms with sqrt(x-1). U should pretty quickly realize that, after an incredibly common partial fraction decomp, the integral is expanded into the leibniz formula for pi and the alturnating harmonic. Solution: ln(4)+pi-4
I dont get what happened at 23:26 when you divided by 2 and it transformed into the guassian integral. how do you calculate e^(-x^2 - xp)/(1+e^-px) = e^(-x^2) / 2? And 26:02 I don't really get why you mentioned trig sub. I saw this and knew immediately it had to be integration by parts, but since you mentioned it, does that mean there are cases where you would have to force a square, even when it doesnt start with x^2+k or k-x^2 or x^2-k? So here for sqrt(x-1) you would say x = sec^2(theta)? when does this apply/make the most sense? 27:09 idk what u mean by "let this be 2cos^2" how can 1+c = 2c^2? ik itd be s^2+c^2+c = 1-c^2+c^2+c = 1+c >:) 32:40 how do u even tell what is f(x) and g(x) 32:55 i have no idea what you mean by "math contest thingy" 39:30 i think u meant to the fourth x, not "of 4x"
I havent fully made a video about some of these techniques yet. For 23:26, I mentally did u= -x. Then the adhesion step: i+i=2i integral trick. The adhesion step is explained in King's Rule Concept. For 26:02, you do IBP first, then trig-sub For 27:09, 1+cos(x)=2cos^2(x/2) is what I meant For 32:40, you would have to experiment, that's also explained in my training series For 32:55, its a popular math contest problem where youre asked to simplify sqrt(a+sqrt(b))+sqrt(a-sqrt(b)). Let it equal to x, then x^2 will cause some cancellation, then solve for x back. For 39:30, yes.
Question 2 actually isn't that bad if you make a clean observation. Subbing u = ln x, you get u^10 * e^(2u) and the bounds change from -inf to 0. Then with integration by parts, your antiderivative will have the form P(u) * e^(2u) + C where P(u) is a polynomial (you don't have to actually calculate it). Since bounds are -inf to 0, it simplifies to P(0) - 0 = P(0) which is just the constant term of the polynomial, which equals 10! / 2^11
The third integral in this video is how to transfer two roots to quadratic formula ?I think there is 8:26 a mistake ? Can you show some hint here if it's correct?
19:41 (problem 15) i'm pretty sure this diverges?? I spent like a full day trying to solve it, not realizing this was for april fools. I would greatly appreciate a solution in another video or if anyone in the comments has one
It actually does converge. Computing the limit of (cos(x/sqrt(n)))^n is very tricky tho cuz u can easily mess up. But it should become a Gaussian type integral.
Well... ..... .... .... .... .... .... .... .... it requires a lot of robloxhacking into their files, and of course MIT being very good at cybersecurity, I had no choice but to recreate a simulation of MIT Integration Bee problems and pretend that they are official problems for 2025 lol
Now that it's April 2nd, I can finally explain that THIS IS NOT FROM MIT INTEGRATION BEE!!!
As a problem writer myself, PLEASE DO NOT ACTUALLY LEAK REAL PROBLEMS!
That is cruel and the amount of work into problem writing just goes into waste. So please, I do not encourage leaking competition problems.
The following set of problems in this video are mock problems for people to practice, learn, and prepare for MIT level integration bees.
In this case, this video showcases MIT Integration Bee Training Mock Problems.
I will say, I made this problem bank way too accurate and realistic, so I don't blame others for reporting posts from different sites.
In fact, huge props to the math olympiad communities for taking any leaked problems down as fast as they can.
I technically deserved that temporary lock from AoPS to be honest xD
Thank you everyone and I hope these problems help practice for olympiad level integration bees!
??? 🤨
What kind of joke is that to beggin with???
Lmao you totally got me
25:58 Take the tyalor series of ln and cancel out terms with sqrt(x-1). U should pretty quickly realize that, after an incredibly common partial fraction decomp, the integral is expanded into the leibniz formula for pi and the alturnating harmonic. Solution: ln(4)+pi-4
You are a genius 👏 🙌 ,please keep going with little extra explanation 👍
33:21 huh for this one you can also do u=x+1/x which leads do a e^sqrt(u+2) which isn't too hard to do
I dont get what happened at 23:26 when you divided by 2 and it transformed into the guassian integral. how do you calculate
e^(-x^2 - xp)/(1+e^-px) = e^(-x^2) / 2?
And 26:02 I don't really get why you mentioned trig sub. I saw this and knew immediately it had to be integration by parts, but since you mentioned it, does that mean there are cases where you would have to force a square, even when it doesnt start with x^2+k or k-x^2 or x^2-k? So here for sqrt(x-1) you would say x = sec^2(theta)? when does this apply/make the most sense?
27:09 idk what u mean by "let this be 2cos^2" how can 1+c = 2c^2? ik itd be s^2+c^2+c = 1-c^2+c^2+c = 1+c >:)
32:40 how do u even tell what is f(x) and g(x)
32:55 i have no idea what you mean by "math contest thingy"
39:30 i think u meant to the fourth x, not "of 4x"
I havent fully made a video about some of these techniques yet.
For 23:26, I mentally did u= -x. Then the adhesion step: i+i=2i integral trick. The adhesion step is explained in King's Rule Concept.
For 26:02, you do IBP first, then trig-sub
For 27:09, 1+cos(x)=2cos^2(x/2) is what I meant
For 32:40, you would have to experiment, that's also explained in my training series
For 32:55, its a popular math contest problem where youre asked to simplify sqrt(a+sqrt(b))+sqrt(a-sqrt(b)). Let it equal to x, then x^2 will cause some cancellation, then solve for x back.
For 39:30, yes.
@@Silver-cu5up Alr epic, thank you
Question 2 actually isn't that bad if you make a clean observation. Subbing u = ln x, you get u^10 * e^(2u) and the bounds change from -inf to 0. Then with integration by parts, your antiderivative will have the form P(u) * e^(2u) + C where P(u) is a polynomial (you don't have to actually calculate it). Since bounds are -inf to 0, it simplifies to P(0) - 0 = P(0) which is just the constant term of the polynomial, which equals 10! / 2^11
it wasnt hard at all you can just create a genral recurrence relation of something like I(n) = -nI(n-1) and solve it
silver the hedgehog doing integration is not something i expected to see today
ig problem 17 is 8x^3/3+23x^2+88x+c... just shifter over some rows and culums with subtraction which keeps the det unaltered
I didnt know a nice way of solving that one, so i just skipped it xD
I got -6x^2 - 36x + c,I subtracted 1st row from 2nd and 3rd, and then first column from 2nd and 3rd.
For 16th you can write f(x) = tan(tan^-1(x) + pi/3)
So f(f(f(x))) = tan(tan^-1(x) + k*pi) = x.
Nice!!
Very good questions! Greetings from turkey❤
Arrabhaan! (I think thats how u pronounce it my apologies lol, my VRchat friend is definitely gonna dishonor me xD) Thank you!!
Hi I just discovered your channel and it's great. Question on problem 18 23:15. Where does p - 1/p = 1 come from? Thank you!
Its a golden ratio identity
@@Silver-cu5up I mean the problem doesn't state it as a condition. Or is this part of the April 1st joke?
@@Silver-cu5up Oh! Is it understood that in things you write phi represents the golden ratio? I'm new.
@@Namo_Amitabha2024 yep! Thats just how I write the golden ratio.
@@Silver-cu5up ok got it. Thanks!
6:13 it's ALWAYS THAT. Anything BUT integrating
The third integral in this video is how to transfer two roots to quadratic formula ?I think there is 8:26 a mistake ? Can you show some hint here if it's correct?
Oh crap, i forgot the constant should have an x!!
@Silver-cu5up literally I spent 1 hour just to get something about this step ,but only my brain was completely frozen
i think that in ques no 12 of semi finals the limits are going out of the domain of function there
Oh crap they are! Thank u for that!
Why do i watch this every year?
9:11 what about the 1 :( it got left out of the integration
OMG I DID ;_;, thank u for catching that!
holy shit u smartass
19:41 (problem 15) i'm pretty sure this diverges?? I spent like a full day trying to solve it, not realizing this was for april fools. I would greatly appreciate a solution in another video or if anyone in the comments has one
It actually does converge. Computing the limit of (cos(x/sqrt(n)))^n is very tricky tho cuz u can easily mess up. But it should become a Gaussian type integral.
How did u go from step 1 the 8-5 to the 2nd step wit the …? Like in the 1st problem
I did zero-substitution. 0=(x^2+4x)-(x^2+4x)
Now applying it with 8-5 gives us 8-5+(x^2+4x)-(x^2+4x) = (x^2+4x+8)-(x^2+4x+5)
if you knew the gamma function you would be able to do #2 in your head ;)
Ah u right xD
im new to all this. how does the gamma func do that
@@darcash1738 i made a video on gamma function in intermediate training
Letting u=ln(x) then w=-u and t=2w turns it into a gamma function.
I was about to comment this myself! Very simple solution with 3 steps and inductive reasoning.
Shout out to the unilateral Laplace transform
How did you get the 2025 questions????
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it requires a lot of robloxhacking into their files, and of course MIT being very good at cybersecurity, I had no choice but to recreate a simulation of MIT Integration Bee problems and pretend that they are official problems for 2025 lol
Can u just keep keys !!
What program do you use to take notes?
I dont really use any programs to take notes, I take notes handwrittenly. But in the video, I use MS Paint as my whiteboard.
As a Gcse maths student, wtf
Do you offer answers to this material?
I do not have the solutions unfortunately ;_;
@@Silver-cu5up I get it. Margins are too narrow.
40:55 i got 1/2 after creatung a riemamn integral out of nowhere wondering if anybody for the same answer?
its pi/2
Should be pi/2 yea
Bro keeps cooking like how do you do it
FREE SILVER 2024
I believe its just a temporary lock on my AoPS account, huge props to them for investigating, but if I am banned permanently, rip ;_;
This s...t is easy as f...k
YESSIR!
I can't get why you left the problem 2.4 unsolved. This continuous fraction is just a constant with respect to x, isn't it?
I believe so, I just don't remember what constant that is