A beautiful calculus result derived using Feynman's integration technique

Here's another wonderful integration result derived using Feynman's technique and basic complex analysis

[@3manthing]

"Hypotenuse prime" and his sidekicks "Catheti", against evil "Megasharpener" and his henchmen "Erasers".😂

[@hahazns]

This has to be the most chad KZbin channel of all times. No better way to earn respect than conquering those beautiful integrals.

[@zunaidparker]

Holy crap! You're almost up to 20K subscribers...when the hell did that happen! MASSIVE congrats and here's to 20K and beyond!

[@maths_505]

Thanks mate Yeah I just wrapped my head around this a couple days back😂 I was super occupied with house hunting and then moving. Feels awesome alhamdullilah. Thanks alot for all the feedback....its always helpful when planning future videos

[@andy_lamax]

I'd like to let the composers of this that, the efforts made to make this integrand an even function didn't go unnoticed

[@maths_505]

It was worth the result😂

[@SuperSilver316]

You can do this with a Laplace transform I believe also! Cool that the golden ratio comes out of there.

[@northmirko]

Excellent English pronunciation, excellent math.

[@MathOrient]

I love your integrals man.

[@lucidreconalt3229]

Honestly I was waiting the whole video to see if you'd remember to multiply by 2 at the end 😂😂

[@OunegNebty]

I was afraid too !

[@PeterParker-gt3xl]

Awesome teacher.

[@MrWael1970]

Very interesting integral. So, the solution is pretty

[@امینظاهرزاده]

Hi My master How find than numbers complex larger?

[@angrybhalo1671]

Love from India bro

[@manstuckinabox3679]

I put t on e^x2 and used sin squared's relation to cos2x to turn it into something plus something we solved previously on the channel, half way through I was like , hey putting a t in sin^2 would reduce it's power and also turn it into the imaginary part of something we solved, then proceeded to laugh.

[@holyshit922]

It can be done without Leibniz rule Firstly integrand is even on interval symmetric around zero then 2(sin(x^2))^2 can be expressed as (1-cos(2x^2)) and we can integrate by parts Later complex exponentials can be useful

[@illumexhisoka6181]

Is there a case where we can't change the integral and the derivation sign or the summation sign

[@maths_505]

We can only perform a switch up if convergence is satisfied

[@illumexhisoka6181]

​@@maths_505 how do we check that ? And do you have in mind a specific case ?

[@maths_505]

@@illumexhisoka6181 Dirichlet's convergence theorem is a reliable check. It states that if you have the product of a bounded function and a decreasing function (on the interval of integration), the integral converges.

[@krisbrandenberger544]

Would you please give me the link for the video that has the integral with the same structure but with just the sine term? Thank you.

[@maths_505]

It's in in the playlist for feynman integration

[@krisbrandenberger544]

@@maths_505 Thanks!

[@davidblauyoutube]

Bravo!!

[@par22]

Thanks, that was amazing! What happens if you have convergence problems tho? Lots of integration by parts?

[@maths_505]

If the integral diverges then we can't exactly solve it....some exceptions can be made for the cauchy principle value but other than that there isnt a solution.

[@Vanessa.W]

Sorry if this is a dumb question, but when can’t you switch the derivative and integral signs?

[@maths_505]

It's not dumb...it's an important question...if it the integral function doesn't converge, you can't make the switch up.

[@neilgerace355]

Now all you have to do is find an integral problem whose solution includes the Euler-Mascheroni constant as well :)

[@maths_505]

Check out the video I posted 3 videos ago

[@Calcprof]

Im( i times stuff) = Re(stuff) would simplify arguments

[@7calculus]

The square root of 1-2i is supposed to have two answers no? Sir, why didn't you choose the other?if you had chosen the other, the final answer would be ( -sqrt(pi)/2)(sqrt(phi) +1). How to know which one is right?

[@zunaidparker]

The rigorous way is to carry both solutions then check at the end which one is valid and which one is extraneous. The negative result is extraneous because you're integrating a positive function, so the result must be positive.

[@maths_505]

Look at the integrand: you're just integrating the product of positive functions so the negative solution is extraneous.

[@UnknownGhost97]

I got the answer as 2 pi and 0 I feel both answers are wrong Can u verify my answer is right or wrong??

[@wagsman9999]

Whoa!

[@brabhamfreaman166]

Hypotenuse PRIME-Prime-prime-‘rime-‘ime-‘ime-‘ime-‘… This was my best impression of an echo via prose. But now I see some far cooler comments on this part of the video…ho-hum

[@skyblue4558]

You are only uploading integral questions. How about expanding and trying some other types of math questions?

[@maths_505]

Integrals are pretty much the primary source of dopamine for applied mathematicians😂...other than DEs ofcourse.

[@skyblue4558]

@@maths_505 i mean other than calculus. Just suggesting because all your videos are just about integrals.

[@maths_505]

@@skyblue4558 I plan on uploading courses on math undergrad courses soon

[@skyblue4558]

@@maths_505 great

[@rafiihsanalfathin9479]

Nah integrals are fine, there is a lot of other math videos from other youtuber

[@Menon-xk9kc]

Can any jee aspirant solve this??

[@mrQueue78]

Okay cool

[@thomasblackwell9507]

sir; Please stop being self-depricating or belittling yourself or your national state. Just because you find it difficult to pronounce a word does not give you the right to blame it on the state. I am sure if you heard my Arabic you would laugh at me until the cows came home. You are a teacher please understand that the material is what is important. Don’t give your students cannon-fodder against you! Respectfully yours

[@maths_505]

Thank you dear friend. And don't worry, I'm not ashamed of such pronunciation; I only point this out from time to time to add a touch of light humor 😂

[@thomasblackwell9507]

@@maths_505 Dear friend, sir, esteemed teacher; You are in a position of authority and if you are trying to get gainful employment as an educator then you must understand that this is not a joke. If I was an employer I would be examining your channel to see how well you interacted with the students. An educator who realizes that he makes mistakes is one thing but to go to the point of degrading oneself or country is another!

[@cycklist]

Are you suggesting they speak Arabic in Pakistan? That's very wrong.

[@thomasblackwell9507]

@@cycklist I apologize but when I greeted the teacher it was in Arabic, however limited it might be. I mean no disrespect to anybody or nationality.

[@Bruhong99]

Bruh 😂