Lobachevsky's formula: kzread.info/dash/bejne/dKVptqRvk720nso.htmlsi=ZeWTFxTdcQtlN8iy 15 percent off everything using the code MATHS505 on Advanced MathWear: my-store-ef6c0f.creator-spring.com/ Complex analysis lectures: kzread.info/head/PLVkOfIPb514EP3CjWQQ-JmKpIiNoEUS0k&si=rdmwOkQ6Vxg64yrE If you like the videos and would like to support the channel: www.patreon.com/Maths505 You can follow me on Instagram for write ups that come in handy for my videos: instagram.com/maths.505?igshid=MzRlODBiNWFlZA== My LinkedIn: www.linkedin.com/in/kamaal-mirza-86b380252

@YGHF

5 ай бұрын

Hi. Ty for the video If you don't mind me asking, what's the app you use for this vid? Thanks!

@maths_505

5 ай бұрын

@@YGHF Samsung notes

I yearn for the day for which Maths 505 pronounces "Lobachevsky's formula" in a thick Russian accent.

@maths_505

5 ай бұрын

I'll make the whole video in a Russian accent next time homie😂

@daddy_myers

5 ай бұрын

Oh let's FUCKING GOOOOOOOOOOO WOOOOOOOOOOOOO 🔥🔥🔥🔥

@jannesfilgerdamm1419

5 ай бұрын

That would be sooo cool haha xd

@giuseppemalaguti435

5 ай бұрын

Con la proprietà degli integrali ,che io non conoscevo(grazie!!)..risulta I(a)=π/2arcsina+π/2(ln(1+√(1-a^2))-π/2ln2...perciò I=I(1)=π/2*π/2-πln2/2=π^2/4-πln2/2

Amazing. MATLAB's having trouble just integrating this numerically, and you made it look almost easy analytically ... almost.

btw - i like the graphs in the thumbnails, please keep it up.

It is very interesting solution. Thanks indeed.

Beautifully devious, as usual. When you interchange limits it would be good to mention the monotone convergence theorem or the dominated convergence theorem or whatever is needed to justify things.

@maths_505

5 ай бұрын

Or just show the graph in the thumbnail 😂

How could you put the total derivate under the integral sign, also change it to a partial derivate?

very nice approach

Hey I just was wondering, what program/materials do you use to draw on your screen like that? the style looks sick

@maths_505

5 ай бұрын

It's a galaxy S6 tab with an s pen

Excellent!!

How do you know where to put alpha?

Whay about the integration limits when you do the u = tan(x)?

Amazing 😊

Man you scared me 😅 i was about to close the video and i heard someone screem "WAITE"

When you said "Wait!", It took me a little bit by surprise, and I thought for a second your next words would, be "make sure to like and subscribe, before you leave."😂

Non ricordavo quella formula..grazie

You are the best one 😊❤

@maths_505

5 ай бұрын

Thanks bro❤️

I was wondering if you could some day solve some system of DE or some PDE. Anyways you are amazing, and keep the good work mate

@maths_505

5 ай бұрын

Yo that is actually a brilliant idea cuz I haven't done a single video on that ever since the channel started.

How do you come up with the placement for your alpha in I(alpha)

@maths_505

5 ай бұрын

A cancellation often helps. Like I saw the cosines cancelling out. Even if no cancellation happens, getting rid of the log term was helpful so that's a major factor.

@vincentbatens7656

5 ай бұрын

@@maths_505 ye thats fair, thanks

Maths 505, Thanks for the Integrals. Instead of simply directly ‘solving’ an Integral using any of the ‘Integral-Solving-Techniques’, I would like to first understand how the ‘PLOT’ of the Integrand looks like between the given Limit-Ranges in the problem, and also certain other interesting ranges ; and then, solve the Integral by some form of Geometry-Technique, and then, finally proceed to solve the Integral (using Integration Techniques) : - all this, so that we first get a ‘FEEL’ of WHAT we are actually solving for, atleast in a Fuzzy sense - which might then provide us with ideas of which all Applications, such (/ similar) Integrand Expressions might find use in. Such end-use Applications (ie, the Domains), would then probably automatically ‘lead us’ to a more preferred way of solving the Integral (like for eg, by applying Cauchy’s Residue Theorem, or by Substitutions, or by some other Trick etc). For SIMPLE Examples of this ‘PLOT / Geometric’ method, pl refer to “Mathalysis World - Prakash Pant”’s Vdo : “Solving integrals GEOMETRICALLY in 3 seconds” - for eg, inspect the Screen at 49 s. In this connection, I wonder if you (Maths 505) could re-inspect many of yr Integrals’-Videos, and first, show also the ‘PLOT’ of the Integrand - preferably in various interesting Limit-Ranges {somewhat like the Plots, that Wolfram Alpha (Wα) provides in it’s Output}.

@peter9325

5 ай бұрын

To start with, you (Maths 505) may want to perhaps initially look at these Vdos of yrs first, and then if really practically possible, you might want to edit many of yr other Vdos too ? : {I have had only a quick cursory glance at some of yr vdos ; later, in my FREE time (when ?), I would like to go thru them in DETAIL.} : 1) Yr Vdo : “MOM! I found another golden integral!” - dt Mar 19th 2023 : For eg, inspect the Screen at 3-32 m : Would like to see a Typical PLOT of the Top ‘I’ Integrand and Integral (with Limit Ranges 0 to ∞ ; and any other interesting / revealing Limit-Ranges too) - first, BEFORE applying any Substitution (ie, in the ‘x’ world) ; and later, the PLOT WITH Substitution (ie, in the ‘u’ world). This way, one could quickly, fuzzily, also understand the Mapping correspondence between the diff variables. 2) Yr Vdo : “A RIDICULOUSLY AWESOME INTEGRAL: Ramanujan vs Maths 505” - dt Mar 26th 2023 : For eg, inspect the Screen at 1-19 m : Would like to see a Typical PLOT of the Top ‘I’ Integrand and the Integral, PLUS also some Top 2 Typical / Common Egs of the Infinite Sum expression for f(x) ; PLUS also the relation to the Gamma Fn preferably Geometrically. 3) Yr Vdo : “Feynman's technique is unreasonably OP!” - dt Dec 12th 2023 : For eg, inspect the Screen at 1-58 m : Would like to see a Typical PLOT of the Integral I(α) for typical values of say, α = 1 (as reqd in this Eg), but also at some other interesting values of α (ie, at other than 0 or 1) 4) Yr Vdo : “How Ramanujan proved his master theorem” - dt Dec 16th 2023 : Not just a Typical PLOT of the Top Mellin Xform Integral, but also some 2-3 Typical / Common Egs of the Infinite Sum expression for f(x) - for eg, inspect the Screen at 1-32 m. PLUS also the relation to the Gamma Fn (in this Example), preferably Geometrically.

@peter9325

5 ай бұрын

Some good useful Books : In my younger days, I used to refer the foll 3 books quite often - specially for Maths’ Special Functions, Integral-Expressions and Constants etc : {Providing this List of Books - in the hope that it might be useful for many readers} : {I have also given below the Year of Purchase, because I am not sure if these books might be easily avail now, and from the same Publishers.} : a) “HandBook of Mathematical Functions - With Formulas, Graphs and Mathematical Tables” - Dover Publications, NY - Not sure of the Edition - 9th or 10th ?, but I had purchased in Mar 2004. b) “Table of Integrals, Series, and Products” - 6th Ed - Academic Press - I had purchased in Oct 2004. c) “Mathematical Constants” - by Steven R Finch - RePrint of 2004-05 - Cambridge Univ Press - I had purchased in Aug 2006.

5:24 bro missed the square term twice , its like when you are so soaked in integration that you forget wth is going on

5:50 missed the opportunity to call it pi-riodic

@maths_505

5 ай бұрын

YOOOOOOOOO!!!!! Noted for the future!🔥

Isnt it just arcsec at the end? Why arcsech?

@maths_505

5 ай бұрын

Look at a table of integrals and you'll find out why.

Absolutely beautiful

Jajajaja incredibleee... The besttt o f the world

Wait! I thought integral_0->inf(dx*f(x)*sin x/x) = 1/2*integral_0->pi(f(x)*dx), not integral_0->pi/2(f(x)*dx). Therefore the end result should have been I=F(1)=pi/4*(1+ln 2)

@maths_505

5 ай бұрын

Check out the link in the pinned comment. It's a video proving both versions of the formula (it is probably the best proof video on KZread)

@julianwang7987

5 ай бұрын

​@@maths_505 the two formula are equivalent only when f(x) is symmetric wrt pi/2. The difference in end results shows that your version of the formula is no good for this problem.

The answer is infinity

that value of c really looking like the integration of log(cosx) 🧐

@maths_505

5 ай бұрын

Value of c???

@thefirminator

Ай бұрын

​@maths_50 13:49 constant of integration dawg

Log2 appears again...

It is always surprising (infuriating ) to see everyone use feynman tric without proving its validity while feynman trick can often fails

@Yougottacryforthis

5 ай бұрын

You mean the conditions needed?

I miss lemniscate ctant

@maths_505

5 ай бұрын

Me too buddy 😥 Thankfully I have one penned down for the holidays🥳

Mathematica complains that " The integral of tan(x)log(cos(x)+1)/x does not converge on {0,Infinity} " which is an interesting point, don't you think?

@maths_505

5 ай бұрын

Yes but analysis of the integrand along with it's graph (not to mention Wolfram alpha) point towards convergence. Also, this isn't the first integral I've solved that Mathematica couldn't 😂

@RalphDratman

5 ай бұрын

@@maths_505 How can you be sure you've got it right? Differentiate?

@RalphDratman

5 ай бұрын

@@maths_505 And what did you learn from Wolfram Alpha?

@maths_505

5 ай бұрын

@@RalphDratman if I remember correctly, it returned a solution. Though I'm not sure if that was a closed form or not.

@maths_505

5 ай бұрын

@RalphDratman for the integrand: The tangent function has a simple pole for x=(2k+1)π/2 where k is an integer. The log term has a zero at each of those values so the limit of the integrand as x approaches (2k+1)π/2 exists and can be verified to be zero. For x=0, again the limit of tan(x)/x exists and is zero. So there's nothing wrong with the integrand so far. A look at the graph shows that the function and it's oscillations damp out quickly which alleviates fears of divergence. Finally, the result is compared with the output generated by Wolfram alpha. In case Wolfram alpha fails to generate a nice closed form, we can check our closed form numerically. And that sir is how I confirmed that I solved the integral correctly.

Another day, another integral butchered by Feynman's technique.