MIT Integration Bee Mock 2025 Finals Solutions - Part 1

[@kom1i]

john integral himself would be proud

[@Babyshark-co8ks]

I just recognized that problem 1 polynomial was just the 5th Chebyshev Polynomial

[@prioski]

This is beautiful. Made my day

[@Samir-zb3xk]

For question 3: integration by parts then a trig sub yields -πln(2)/2 + (0 to π/2) ∫ ln( 1 + sin²(x) ) dx I solved the general form of this remaining integral on my video here: kzbin.info/www/bejne/iXesfZWLd7OGbJI

[@fhffhff]

0,5(sin(x/2^(n-2))-sin(x/2^(n-1))) 0,5(sin(x/2-¹)-sinx+sinx-sin(x/2)+..) =0,5sin(2x) -0,25cos(2x)|(0;π/2)=0,5

[@saraandsammyb.9599]

Hey Lucas I love Silver and I loved your vid as well!! Is there any way that you have like a master sheet of the rules you need to know to be very good at integration ie. Catalans constant and its series representation, eulers reflection formula, glassers master theorem etc.? I find it kind of hard as a newbie to advanced integration to keep track of them all? If you don’t have one, would it be possible if you could help me make one? Thank you!!

[@LukasTrak]

@@saraandsammyb.9599 Yeah I’ve got a page in Obsidian with integration notes that I add to over time. I recommend you do the same and add anything you think would be important to remember.

[@krishpandey854]

@@LukasTrak yeah I face the same problem. I am very good at the basic techniques- substitution, by parts, reduction/recursion, use of symmetry/periodicity of the function, occasional use of inverse functions but I suck at the more advanced stuff like series/feynman/glasser's/complex representation

[@saraandsammyb.9599]

@@LukasTrak Ok, thank you! Would it be possible that you could share it with me?

[@LukasTrak]

@@saraandsammyb.9599Maybe in the future, it’s pretty messy haha

[@LukasTrak]

@@krishpandey854Check out dr3213 on youtube, he has videos on all of these

[@RehanZafar381]

Great video👍

[@Tosi31415]

crazy good

[@krishpandey854]

Can I get a source for the answer key of the exercise??

[@LukasTrak]

@@krishpandey854 Unfortunately there isn’t any.

[@krishpandey854]

@@LukasTrak is it just me or do the questions seem harder than the actual integration bee. I solved the semis and the finals and the exercise was harder for me than the 2023 integration bee

[@fhffhff]

$(-1;1)xln(1+(cosx)^sinx)dx=$(-1;1)(-xln(1+(cosx)^sinx)+xsinxlncosx)dx =$(-1;1)0,5xsinxlncosxdx=-cos1lnco s1+cos1-sin1+0,5((sin1-1)ln(1-sni1)+(sin1+1)ln(sin1+1))