you do this integral, not me (Harvard MIT math Tournament 2011)

you do this integral, not me (Harvard MIT math Tournament 2011)
Here's the problem file: hmmt-archive.s...
and the solution file: hmmt-archive.s...
‪@bprpfast‬

[@SMB8037C]

day 2 of asking steve to upload "when calculus teacher uses d as the variable"

[@createyourownfuture5410]

Why?

[@SMB8037C]

@@createyourownfuture5410 d/dd (d^2)=... u get the idea

[@Anmol_Sinha]

That video would be interesting to watch.(I think he has done similar videos in the past but not sure whether he used d as a variable in those ones)

[@1224chrisng]

so let's find the antiderivative of (ln x / x)^2011 first
so if we let u = lnx, and du = 1/x dx, we'll have u^2011 dx, which we can indefinitely integrate to get (1/2012)(u^2012), which is also (1/2012)(ln x)^2012

[@SISKCERTWaJaVlogs]

and therefore it diverges

[@Catilu]

"You do this integral, not me"
Actually I was never gonna do you

[@superiorspyder]

lmao i hope this blows up

[@LuciferAmoyai]

bro🗿

[@applealvin9167]

Never gonna give you up

[@adamsulc3343]

I did it without gamma function. Let u=ln x, than we have an integral from 0 to inf (e^-2010u * u^2011) du. Then I did DI method and all terms vanished except the last term. So the answer is 2011! / 2010^2012

[@SMB8037C]

same bro

[@arpankoley4256]

Same 👍

[@Jha-s-kitchen]

which function did you take as D and which as I ?

[@nathanjiang100]

IBP is how you would calculate gamma(x) so unfortunately you wasted some time reinventing the wheel by not utilizing it. All the steps were correct though.

[@Jha-s-kitchen]

@@nathanjiang100 Does he has any videos on Gamma function.. I keep listening about this but don't know what it is?

[@applealvin9167]

2011!/2010^2012
let x=e^u then let t=2010u
There should be a gamma function at the end
Correct?

[@adamsulc3343]

I got the same result! 💪🏻

[@applealvin9167]

@@adamsulc3343 Nice!!!

[@nathanjiang100]

yeah my first instinct was to let u=lnx and i used the same steps after some manipulation

[@DokterrDanger]

Others: *solve*
Me: *GET THE WOLFRAM ALPHA GOIN' BABYYY!*

[@adamsulc3343]

Wolfram cannot solved it unfortunately😥

[@nilanjanghosh9285]

A problem on gamma function
The ans is --> (2011)!/( (2010) ^(2012) )

[@SISKCERTWaJaVlogs]

pov: no gamma function needed just u sub

[@SISKCERTWaJaVlogs]

If i can solve dat shii in my head and im trippin or this just an easy one

[@tanujabudhori]

How to get indefinite integration of this function inside definite integrarion?

[@govindrajanverma4081]

Tends to negative infinite.

[@theimprudentman7272]

How? Actually the denominator 2010²⁰¹²>>>>2011! So the answer tends to 0

[@ssdd1316]

since when did i sub?

[@mikuculus3720]

What level of math is needed to solve this

[@alham9656]

Calc 2

[@ΑΝΤΩΝΗΣΠΑΠΑΔΟΠΟΥΛΟΣ-ρ4τ]

First

[@ΑΝΤΩΝΗΣΠΑΠΑΔΟΠΟΥΛΟΣ-ρ4τ]

@Meelo MaBoi :(

[@stevemonkey6666]

If you posted first then me replying to your thread makes me the first poster aswell

[@yashrajyaduvanshi7767]

@@stevemonkey6666 Big brain time

[@sahasismandal5643]

Sir you put the value of infinity♾️ -1/12 and done the math in two process with infinity♾️ and other normal process check the value of infinity♾️