Feynman would be proud. A Wonderful Generalized Integral.

[@NPCooking69]

Thanks for watching

[@sahmaddast3655]

what's up papa flammy, love the content like usual. I got a question about the merch though. What happened to the engineering clock?

[@twistedsector]

*Screams in Laplace Transform*

[@eugeneimbangyorteza]

hahahahah exactly what i thought

[@FF-qo6rm]

Interchanging the Re() with the integral was bonkers! Never knew you could do that!

[@69erthx1138]

Euler said it, I believe it, that settles it:-).

[@DavidPumpernickel]

Literally one of the craziest things ive seen in a while. Very cool trick

[@xulq]

For explanation search in yt brap sound effect

[@jadegrace1312]

It's kinda standard tbh, he does it a lot

[@SitremChannel]

Watching you solving integrals really stimulates me to work harder, for some reasons. Greetings from an Italian physics student

[@DavidPumpernickel]

NO DONT EAT THE CHALK FLAMMY WHAT

[@pinklady7184]

We need to send him edible chalks with flavours like fruits, white chocolate, vanilla, etc.

[@AlgeArid]

Papa Flammy's slowly losing it in quarantine

[@DavidPumpernickel]

;_;

[@user-wu8yq1rb9t]

One of the best Opening ever, actually Grand Opening .... I love you Lovely Papa. Great video ... Thank you so much 💕

[@watertruck9893]

Idk why I’m subscribed to this channel eventhough I haven’t even learnt calculus or integrals yet.

[@edwardgaming466]

Lmao same! I also want to do this kind of stuff but I haven't even learn calculus yet. Still got a very long journey.

[@TrueLegoXman]

You'll be ready when you take it.

[@thereasonabletroll68]

.... wat?

[@computer-love]

check out 3blue1brown's "essence of calculus" series, it's a great introduction to some of the fundamentals

[@might_e]

It’s a nice look into how the flow of solving higher level expressions and analysis feels and works

[@guillermobarrio55]

I would apply the definition of Laplace transform of cosine after deriving with respect to x.

[@saranyamitra9051]

We can also use the division property of Laplace transformation

[@williamky8842]

That’s just the Laplace transformation of a sinc function

[@euyin77]

You could evaluate in the result of the integral obtained in 6:03 directly and that leads to -Re((z + ix)/(z^2 + x^2))

[@Someone-cr8cj]

your videos are an emotional roller-coaster for me. i love it.

[@The1RandomFool]

Very interesting problem. I tried this before watching the video, and differentiated with respect to z inside the integral instead. I got pi/2 - arctan(z/x), which is equivalent to your answer.

[@tszhanglau5747]

Oh sht this is amazing! Looking forward to the next video!

[@gabriel7233]

I love these hard problems with preparation videos because it feels like I'm watching some good Netflix series :D

[@nnniv]

0:17 lmao

[@DavidPumpernickel]

11:00 in EM last semester I lost a mark on a problem set for using the variable as the upper bound :( I'm confused now. Why would this be unreasonable or why is it otherwise okay to do?

[@ChemiCalChems]

He is just avoiding the usage of yet another variable. The variable inside the integral is a dummy variable, meaning the final expression does not depend on the variable of integration at all, because all the dependency is inside the definite integral. Thus, you can really change this variable for anything you want, it doesn't matter what its name is, you are going to end up substituting it for the limits of integration, so it won't end up mattering what the variable's name is. To avoid confusion, however, it's better to normally use another variable, because if you don't, you might end up confusing the limit of integration "x" with the "x" inside the definite integral, which is a dummy "x". They are not the same variable really, one is a dummy variable, the other one isn't, but they have the same label because why not.

[@ramongallardocampos5241]

it iz what it izzzz

[@DavidPumpernickel]

@@ChemiCalChems riiight i get you... all this time i didn't realise the term in the integrand is a dummy variable smh

[@gabrieleproietti8802]

great video but please, next time I need to see the dumpening part on your t-shirt!

[@knivesoutcatchdamouse2137]

I doubt my question will get answered, since this video is somewhat old, but starting at about 6:05, why are we able to bring e^(-tz) outside of the definite integral, with bounds t=0 and t -> infinity, when "t" is the variable that we *just* integrated with respect to? I thought we HAD TO evaluate the values/limits of the antiderivative with respect to the upper and lower bounds, and that only constants or functions not involving the variable of integration could be pulled outside of the as-of-yet unevaluated antiderivative (unevaluated in terms of the bounds, that is). I very much hope that the statement of my question is clear as it was difficult to formulate in words, and I hope to god that someone can answer this for me. Thank you.

[@manofculture432]

He didn't bring the exp outside of the integral at 6:05, that was the answer of the integral already (if you derived that with respect to "t" you would get the "cos(xt)exp(-zt)" again), he just put the exp(-zt) outside the *Re*() operator. Hope it was understandable.

[@knivesoutcatchdamouse2137]

I have no idea what was wrong with my brain that day. It must have been past my bedtime.

[@likestomeasurestuff3554]

Just curious papa flammy: do you know what your students think of the channel

[@Abhijitdas8710]

Loved your take on this integral..Or we can do in other way if I'm not wrong...the whole integral is the Laplace transform of (sinxt/t)....and L inverse of tan inverse (x/z) = Sinxt/t....done

[@rabiranjanpattanaik686]

3:17 Papa what integration technique you mentioned?

[@dozzco2827]

Loved this video!, Also out of curiosity does Papa flammy feed Andrew Dotson His chalk in his basement

[@neilgerace355]

Really neat work

[@MrRyanroberson1]

a lot of people be talking about sinc here. are there any neat uses for it?

[@PapaFlammy69]

It appears in physics and signal theory a lot ^^

[@joao_pedro_c]

what would happen if the bounds of integration depends on x for this case? how different would be the Leibniz rule?

[@RafaelRibeiro-fo6cp]

kzbin.info/www/bejne/rZzLYoxth5amhdk He made a video deriving the complete Leibniz rule for integrals some time ago, check it out :)

[@Abhijitdas8710]

There would be additional two terms.... derivatives of limits w.r.to x....Lets say limits are "a" and "b" thn terms will be like this db/dx and da/dx....

[@MicheleCaine]

Would not be nice to evaluate the integral from 0 to inf of sin^k(x)/(x)^y dx ?

[@GirishManjunathMusic]

I'm sorry if this is more apparent to actual math boys, but as a humble bio boy, I gotta ask, how can you pull the real function out of the integral when only the cos(tx) is affected by it, and not e^(-zt)? As z could be a complex number, wouldn't it have an imaginary part that would once more split into a -(e^(-at)*(cos(bt) - isin(bt))), where a is the real part, and b the imaginary part, of z; and b∈(-∞,∞)?

[@MonsieurDauphin]

I don't think it's obvious ahaha, my guess is that he intended the domain of z to be only real numbers though. Would have been good to state, I guess.

[@GirishManjunathMusic]

@ゴゴ Joji Joestar ゴゴ yeah his entire solution falls apart if z is a complex number.

[@Dakers11]

Danke papa. Das ist genug fur heite. Always remember, flammy on top with respect to 0(zero) !!

[@tgx3529]

I don't understand this.Papa said at the beginning of the lecture, he did not know why he chose the parameter x. I think ,here is |cos( xt)*exp(-zt)|0. There is this integrant independent on x. I can take x>0. If x0? Only when z>=0, I will get finity integral, it also depends on the type of integral ( for ex (L) integral from sin t/t doesn't exist). The similar situation is whene I chose parametr z, I want finity majorit integral , where integrant is independent on z [|-sin(xt) exp(-zt)|1/100 (for example) , I will see finity majorit integral . If I respect only Lebesgue integrals, there is the problem. On internet is derivation integrals with parametr for Lebesgue integrals.Maybe it uses for Newtons integrals, I dont't know it.....If not, then I don't see any importance this example.

[@mudkip_btw]

Hell yeah what a nice looking thing super excited for this one :D

[@mudkip_btw]

Noiz

[@DavidPumpernickel]

5:40 yay we love shout outs to other math youtubers :'D

[@riakm921]

Fun stuff! I did things by "integrating under the integral", by saying sin(xt)/t = integral of cos(yt) from 0 to x, but it all works out the same way because of the cyclic derivative nature of sin and cos

[@bentn1374]

5:27 no, I luv wen me _waf_ is on top

[@VaradMahashabde]

After you did the intro I thought you just had a jug of sugar syrup

[@zachchairez4568]

That intro ☠️

[@Nadavot]

By changing variable of integration [x t=y], and relabeling [z=x A] you get a simpler integral: \int_0^\infty sinc(y)exp(-Ay)dy As others mentioned, this is simply the Laplace transform of sinc(y). Whice in turn is simply given by int_{z/x}^\infty ds (ℒ{sin}(s))=int_{z/x}^\infty ds(1+s²)^{−1}=arctan(x/z)

[@elshaddai225]

Show that the sum of (m+n)th and (m-n)th term of AP. Is equal to twice the 'm'th term.

[@rbdgr8370]

I got different result when I partially differentiated w.r.t z

[@Jared7873]

hmm... :?

[@eliasandrikopoulos]

Integgeral???

[@DavidPumpernickel]

Hahahaha that Andrew roast. BUT THE WAVEFUNCTION HAS TO GO TO ZERO AT INFINITI MAH BOIS N GRILLS

[@rafaelvaliati3728]

That "good morning" is getting higher and more distorted in every video

[@bk-sl8ee]

Sir I apologize to give u this trouble but please reply, at least. I want to learn maths. (Zero to hero) I don't know calculus, linear algebra. My question 👇 But I want to learn everything about math, all the math up to post graduate/PhD level math from zero. Which books do you recommend sir? (Doesn't matter the number of books it's quarantine time after all, I will give try to all books u tell me; in systematic manner, plz help me. I just need guidance.)

[@guillermobarrio55]

You could start by checking this channel: Vedantu JEE. It is about the preparation for the Indian college entry exams.

[@physicsboy1234]

Nice

[@someonesomeone4099]

What’s with the clock 🤣

[@Jared7873]

Awesome fizzy, fuzzy, timey, wimey!

[@nyuunyuu2704]

Integrals you uploaded can be easily solved also by using Maclaurin series. So even though I am freshman in my university, I could solve almost your problem. Thx for interesting problem.

[@h2_]

I LOVE KITTY CATTIES

[@davidcollin3031]

5:43 am

[@radzieckipjes8687]

ez

[@cycklist]

Zed!!

[@someperson9052]

Ooo

[@ShadowZZZ]

Sigmaballs xD

[@pierineri]

Buy why you guys insist to call that "Feynman's trick". it's not a trick and it is definitely *not* Feynman's. Mathematicians differentiate under the sign of integral since Newton's times. In fact, derivative and ODE have been invented exactly to this purpose. Let a parameter vary and deduce global informations from differential ones.

[@tszchunlau223]

No views? Guess I'm early.

[@cubicardi8011]

I gauss you are