A result you definitely should know
HTML-код
- Опубликовано: 3 мар 2024
- We finally have a proof for the Frullani integral....okay we finally have 2 and that's pretty cool.
My complex analysis lectures:
• Complex Analysis Lectures
If you like the videos and would like to support the channel:
/ maths505
You can follow me on Instagram for write ups that come in handy for my videos and DM me in case you need math help:
maths.505?igshi...
My LinkedIn:
/ kamaal-mirza-86b380252
Advanced MathWear:
my-store-ef6c0f.creator-sprin...
#calculus #math #maths505 #physics #integral #integration #differential #equation #stem #stemeducation #advancedmath #teaching #learning #hustle #everyday #neverstop #passion #education #mathstagram
That intro caught me off guard😢😢😢
Bro what is that accent 😭
Intro by Boris Kamalovsky
Ireland is next on putin's hitlist
nvm just found out you're pakistani i thought you were irish for some reason
@@joeyhardin5903 😂😂😂
that's what maths 505 sounds like when he's not sick
THE SECOND PROOF WAS ABSOLUTE GENIUS WTFF
Kudos on being the only calculus channel in the history of RUclips to be slapped with a “parental advisory” notice!
Yeah, think of what the children may learn out of this! 😂
Best math channel
Best subscriber base❤️
If Integral of f(x) dx from 0 to infinity exists, then the limit of f(x) as x -> infinity must be 0 (assuming integrability and continuity). For otherwise f(x) is bounded away from 0 by at least epsilon for x > M, and the integral diverges.
My boy Frullani finally getting some love
Eagerly awaiting the Leibniz and Feynman accents!
8:03 The limit as x approaches infinity of xy is only equal to infinity if y is a positive real number
Hi,
Very nice result! I prefer the second proof. And I like your "ok coool" as well!
There's merch for that now😂😂
Absolutely stunning proofs
The second one was absolutely crazy
Bro I seriously like your
"OKAY COOOOL"
it makes the video more interesting ❤
11:54
12:12
Very nice proofs. Thanks.
Does it work for a, b < 0 and f nit diffable?
Great video. But for an older man like myself can you illustrate using an example. I'm scratching my head thinking where would I find f(ax) and f(bx) in my engineering calculations.
I'll make some shorts for illustration purposes
Could you please solve Cleo's most famous integral?
I see you added the NSFW tag.
Very good my friend. Very good.
It's a recurring theme now 😂
@@maths_505 why tho
@@math_Nerd-nt2gb I don't know maybe it's cuz these integrals go hard 🔥🔥🔥
This is the only 18+ content I watch lol
Ur insane 🔥
The second proof is much easier and understandable.
The only thing I would suggest is to substitute variable y=b•x , and substitute the parameter c = a/c
So the integral will be
( f(c•x)-f(x))/x•dx
The result would be the same.
I shall remember this elrond my friend
It's a good thing you didn't mention what the video is about in the title... wouldn't want people being able to find it later through search.
With all that happened, I'm surprised that I was able to focus on the maths, and I'm even more surprised that I could understand what was happening
=> Intg log(ax)-log(bx)/x •dx
Intg log(ax/bx)/x •dx ax/bx^2•dx
Intg a/bx•dx Intg a/b•x^-1•dx
Intg [-log(a/b)] ♾️->0, or
Intg [f(a) - f(b)] ♾️->0
🤔 if u examine carefully u can actually make bunch of more cool tricks from the Feyman method he presented
That's an interesting result. However the proofs given here require f to be differentiable, df/dx to be integrable, and in order to apply Fubini (1st proof) or Leibniz (2nd proof), |df/dx| to be absolutely integrable on [0,+∞)
There is a more general proof on the French Wikipedia article, which doesn't need those requirements: f simply has to be locally integrable on any interval of (0,+∞). (click on the "Démonstration" box). fr.wikipedia.org/wiki/Intégrale_de_Frullani
fire accent fire proof
I remember that comment about the accent lol
You sound like my continuum mechanics professor from uni 😂
Nyet, integral is fine
по началу сразу видно: наш! земляк!
This accent doesn’t sounds like Russian, but as I’m Russian, I think it sounds like Spanish :D
0:00-0:55 😂😂😂😂😂😂😂😂😂😂😂
Just take f as 0 and u are done ❤😂
Russian Kamaal is best Kamaal.
Very nice speaking😂😂
Это слишком просто! Есть что то поинтереснее?
Man!! never do that again! I was really afraid that 'everyday mathematics' hacked your channel, I checked the link twice
Who tf is that?
@@maths_505 just take a look at his vids, you will understand ;)
Reverse cowgirl is the best. 😂
*slow clapping*
YEAH! REVERSE COWGIRL!
I thought it is a fake channel
Lol
😭 stop changing voices i get confused if i am in some fake math505 video or real one
The recent swearing and sex references are a sad development that I hope you consider walking back. It's your channel, you do you. But for me, at least, it takes a great channel that I recommended to middle school and high school mathematicians and makes me regret it. Unsubscribed. Bummer. Loved your content!
I'm sorry about that mate. I regularly check my analytics and 80 percent of my audience is aged 18 to 54 with the biggest chunk of that being aged 18 to 34. I find it interesting that you recommended the channel to middle schoolers but I just don't think my channel would be the least bit useful for them. However your comment has resonated a bit so I might as well take it into consideration.
I appreciate the thoughtful reply! I know kids who are the super-math enthusiasts - doing calculus in 8th grade, Art of Problem Solving, etc. I don't doubt the vast majority of your audience is not going to be offended. Thanks for thinking about. Truly do love the math - and I appreciate the "don't miss leg day" advice. Particularly important for math nerd set!
@@maths_505I think it’s also important to note that even if 95% of your audience is okay with it you might still be alienating the other 5% and I highly doubt people are more likely to watch a calculus video if it talks about sex because I think the kind of people who are drawn to this content are going to be drawn to it either way. Personally I’m usually fine with people openly talking about sex and I honestly think it’s something that should become less taboo however I feel like here it just detracts from the math that I came for.
I feel like I kind of rambled with that but my point is that I doubt people are particularly interested in it and I know there are people who are very uncomfortable with it and it also just feels very unnecessary
First