This integral is too good to be true (the Bernoulli integral)

[@ryankelly9772]

I mentioned you in my application to maths at Cambridge and have my interview tomorrow, Wish me luck 😁

[@maths_505]

Awesome ❤️ I'm praying that you get accepted bro ❤️

[@zanebaker6693]

Same 🤣🤣🤣

[@danielc.martin]

Good luck!

[@theyama2929]

I was thinking of doing the same (mentioning this channel) lol. Really hoping u get in. 🤞🤞

[@swright4171]

Tell us how it goes!

[@manstuckinabox3679]

I'm beginning to be able to solve these problems quite effectively, and this time or methods were 100% the same, I think that's what a one-year subscription to math's 505 gets you, I'm currently celebrating our one-year parasocial anniversary, and what a reward it is to see myself grow alongside this channel. Here's to another year of spamming the snarliest solutions which most of the time don't work, hopefully next year we'll hit that 100k mark.

[@maths_505]

Ah I see that the indoctrination phase was successful 😂 thanks bro.....always great to see you in the comments section.

[@romainblondel8320]

I had heard about this as "Sophomore's dream" and wondered why it was like this ! So thank you for this video 😃

[@matchamitminze]

I’m studying for my calculus II exam and I’m glad I was able to follow through completely! Series and sequences were my favorite unit and so this gives me confidence that I’m going to ace my final. :)

[@MrWael1970]

Very interesting integral. Thanks for your featured effort.

[@qubix27]

Something that really is too good to be true is that the same integral but from 0 to infinity is tantalizingly close to being exactly 2, but falls just a tiny bit short (1.9954...)

[@archinsoni1254]

I'm sure it's one interesting constant like Apery's constant. I devised such series on my own when I learnt that convergent series often give us transcendental numbers.

[@hamazoon.]

3:21 Bro why are you always terribly sorry. The sorry doesn’t have to be terrible.

[@maths_505]

😂

[@dylanelias6812]

Are there more functions like this, where the integral of a function equals the sum of a function?

[@maths_505]

Not that I know of at the moment but I am looking.

[@taterpun6211]

There is integral of real numbers sinx/x = sum of integers sink/k (provided sin0/0 "=" 1) = pi

[@michaelihill3745]

Awesome result!

[@patricius6378]

Really smooth, just as expected. Where's daddy myers tho??

[@daddy_myers]

My heart warms to the realization that I've garnered a cult following. 😂

[@skyethebi]

Can you give us an example where you can’t switch up the integration and summation but the integral is still solvable a different way. I’m just curious what that looks like.

[@giuseppemalaguti435]

Σ1/k^k,k=1,2,3....con serie esponenziale e integrazione per parti

[@justinpark939]

I feel like you can use the reiman sum definition to tackle this but I feel my algebra isn't clicking. Anyone think it is possible?

[@akifbaysal9141]

I guess you also need to add a brief justification on why expansion of e^y where y= -x ln x and for |y|

[@markellacabe7171]

But the series of e^x converge for every value of x right? So you |x| could be greater than 1 and there is no problem. To demonstrate it, take the series of e^x and find the convergence, u will see that the exponential below will always decay

[@akifbaysal9141]

@@markellacabe7171 Yes you are right indeed for e^y special case, but it could have been a different series and y itself is some functional form of x, convergence of a functional form is better checked I guess.. Checking only at x limits then finding the y(x) converges may not be sufficient for some other expansion forms in terms of y..

[@markellacabe7171]

@@akifbaysal9141 yes of course, other series dont converge for any value of x, but i guess that he considered trivial the fact of e^x always being convergent

[@hiiistrex2838]

I KNOW I'm a nerd because of my reaction to cancelling out the factorial

[@michaelbaum6796]

Wow, this is amazing 👍

[@CM63_France]

Hi, As you said : this result is awesome ! (I will never write this word correctly, because the translation from FR gives me another word).

[@nikko2505]

~1.29129

[@EyadAmmari]

Love it.

[@anupamamehra6068]

hi maths 505 how to prove digamma(1/2) = -eulermascheroni - ln(4)

[@maths_505]

instagram.com/p/Cuak4YaNRy9/?igshid=NzBmMjdhZWRiYQ==

[@treyforest1999]

Does this constant have a name?

[@maths_505]

Unfortunately no

[@212ntruesdale]

I’m a completely amateur mathematician, enjoying math problems the same way others enjoy crosswords. Indeed, that’s what math problems are to me, puzzles. The other thing I love about math at this level is being able to speak a very complex second language. Not to brag, but I feel pretty good having a rare skill. It might not be all that useful in and of itself, but, if confidence is anything, nothing will give it to a person like being comfortable with math.

[@zunaidparker]

OK but what's the answer? Anything special or clever? Great result regardless.

[@maths_505]

Unfortunately there's no closed form but I'm actually happy about that here 😂 the final equation is beautiful.

[@Calcprof]

Wow.

[@MatthisDayer]

Wait what you have 250 videos... And I watched them all, wtf

[@nicolascamargo8339]

Genial

[@violintegral]

lol did you make the thumbnail wrongly start the sum at x = 0 on purpose?

[@maths_505]

I have no idea what you're talking about😂

[@maths_505]

Fixed it