Kkkkk

Lol

For some reason , “lol” looks like mod(0)

@@camkiranratna do you mean absolute value?

@@deltaspace0 Absolute value is also called mod in some places.

hahahahaha! honestly, that wasn't planned.

blackpenredpen I just realised after reading this...

me 2 lollll

It seemed to me like some sort of band sign like Nike at first

what’s the difference between partial derivative and normal derivative?

I agree, I solved this too in my first course of Applied Mathematics in college where we used complex analysis techniques kzfaq.info/get/bejne/fMxkf7Wdy9LNkmQ.html

Yeah that's true, that's how I learnt it/saw it first

Integrales cerradas en variable compleja?

You can do integrals on complex bounds (lower/upper) 😮? Or is it Real bounds but integrated on Complex functions?

@@louisrobitaille5810 complex functions and complex bounds. Turns out that the path you take *mostly* doesn't matter!

More like when you blink in class :)

but the answer was spoiled in that part :D

when you struggle not to sleep

Idk why was the video cut? lol

Ahnaf Abdullah I wanted to add that explanation why b has to be nonnegative

PompeyDB it is!

it is, is not? It's!

I really enjoy watching you disintegrate! Relaxing and fascinating at the same time. Isn't it!

@@rehmmyteon5016 lmao

Yes, Feynman was a brilliant mind

MeowGrump lolllll this is a good one!!!

asics = "Anime sane in corpore sano," "Sound mind/spirit in a sound body."

Anima not anime (but that's somehow relevant :))))

👌 looks like the partial derivative sign XD

So, it is soul eater then?

.l

Dokuta Viktor trust no one

Dokuta Viktor Ask wolfram.

Dokuta Viktor only if it gives the same answer as what we got.

blackpenredpen what if what you got is by looking at Wolfram????

then don't get things from Wolfram but just check your answer with it.

its not that unexpected though if you look at the function... its just looks very convergent.. (this can ofc be very deceiving)

@@antonquirgst2812 But there's the fact that as x grows larger, it tends to 0 because sin's at most 1 or -1.

@@createyourownfuture5410 yup - totally agree - x grows linear while sin(x) is periodic!

@@antonquirgst2812 Aaaand it approaches 0 from both sides

@@createyourownfuture5410 It actually approaches 1 from 0

Lies again? So fat

How so? What did you notice?

isn't it?

That's what she said

Physicist*

@@juanpiedrahita-garcia5138 lol

Sean Clough yay! I am happy to hear!

lol

I'm familiar with using the Fourier transform to find the integral, but I don't quite see how you'd use the Laplace transform.

@@Sugarman96 - the Laplace transform is what the above video uses when creating his function I (b)

​@@Sugarman96 I'(b) is the same negative laplace transform of sin(x) which you can use to easily find I'(b) instead of doing whatever he did.

yay!!!!

Yes, i did It and i got 10 in my integral calculus exam :') two months ago !

@@MrAssassins117 now 3 years ago lol

@@pranav2119 now 3 yrs and 14 hrs ago.

Wonderful!!!!!!!!

Thank you!!!

bruno edwards Yup, leibniz rule is very powerful.

Paul Montes dr. Peyam is actually going to do that soon

Why would anyone think to add e^x thiugh this COMES OUT OF NOWHERE..what I thought to do was replace sinex with e^ix from Eulers formula..isn't thst smarter and more intuitive? I think he needs to justify where e^x cones from if anything it should be ln x he is adding nkt e^× since 1/× is the derivative of ln x not e^×..

I think you're right. I was thinking the same

Does it help? I am not an expert in the field (yet): en.wikipedia.org/wiki/Leibniz_integral_rule

Hi, this is Zachary Lee. You are absolutely right to be concerned about the convergence at b=0. What you want to do is let b approach 0 from the right. If you want a rigorous explanation, check out Appendix A, on page 21 of this document: www.math.uconn.edu/~kconrad/blurbs/analysis/diffunderint.pdf

Footskills here's the man!!!

Yeah that was a brief explanation haahahhahaha

And here I am again!!! Btw, great explanation!

PackSciences your counter example should be rearranged as (e^(-b x)-1)/x Btw e^(-b x)/x diverges for all values of "b"

elp 486 It’s a definite integral of 0 from a to b, so there’s no area. : )

Hard to justify with those zero to infy limits. ;-)

so, pi/2 \approx inf?

How can you pretend all angles are small? The angle goes to infinity o_O

@kikones34 : Yeah, that's the joke (note the ":D" grin at the end.). But it _does_ work for the _variable_-bound integral int_{0...x} sin(t)/t dt which, by the way, defines the standard mathematical function Si(x), the "sine integral" function, because you can then consider when all angles in the integration are small. If you take sin(t) ~ t then you say for _small_ x that int_{0...x} sin(t)/t dt ~ int_{0...x} t/t dt = int_{0...x} dt = x so Si(x) ~ x when x is small. And a Taylor expansion will show you that that makes sense, too: Si(x) = x - x^3/(3.3!) + x^5/(5.5!) - x^7/(7.7!) + x^9/(9.9!) - x^11/(11.11!) + ... so the first (lowest-order) term is x, thus at small x, Si(x) = x + O(x^3), meaning the rest vanishes like x^3.

@mike4ty4 Oh, sorry, I totally didn't get you were joking. I've been on a KZfaq trip of flat earther videos before watching this, so I was in a mindset in which I assumed nonsensical statements are actually serious and not jokes xD.. D:

LOL! Thanks! In fact, that wasn't planned. lolllll

Thats not a lowercase Delta

Here comes the paid publishing

Jack Chai ok

I also had this question. Anyone can help?

@@riccardopuca9310 Maybe you have to set b>0, but when going back to the original, you let b approaches 0+?

The last step where he solves I(b) for b = 0 is a clever trick to avoid putting 0 into e^-bx. If you've taken diffeq, you can confirm for yourself by solving the original integral with a laplace transform. It'll also answer where the e^-bx came from in the first place

had the same problem - i guess one can make b > 0, and then take the lim as b -> 0 from above on the I'(b) or I(b).. and would still be fine .. but how is presented, has that small issue

The integral over sinc(x) also has a name (since it's not an elementary function), the Si(x) ("integral sine", no the abbreviation doesn't make sense).

What does the c stand for in why it is called a sinc function?

@@carultch it’s just a notation that is used to define sin(x)/x. I forget if there are any special properties to it, but it was used a lot in the signals class I took years ago during my undergrad. I believe I watched this the semester after I took it. Taking a look a bit, pretty much the application we had was that the Fourier transform of a rectangular function is the sinc function. I don’t remember much past that as I haven’t used it for years since then

@@UnOrdelyConduct I found the answer. It is called "sine cardinal". Not sure what cardinal would mean in this context, or if it has anything to do with cardinal numbers, but that's why it is called sinc of all possible names.

Does theta stand for anything particular in Greek, relating to angles? Or is it just an arbitrary letter that has historically been used for representing angles similar to how x and y represent Cartesian coordinate variables? Probably, the reason x/y/z are used for representing Cartesian coordinate variables, is that it is the trio of neighboring letters in the alphabet, that is LEAST likely to stand for anything in particular, and therefore they are letters used as wildcards.

me too

You got it ,me too

Thank you!

Deanna Baxter I always just plugged in infinity. Didn't lead to any misunderstandings. It's more cumbersome to take the limit, though it's technically correct. You first introduce indeterminate forms in order to avoid issues.

Rudboy I agree, sadly sometimes students won't be lucky enough to get a grader who will be forgiving. I one time did that and the grader goes "While your final answer is correct, you can't just set something as infinity" There was another part of the problem where I got the answer correct, and they go "your answer in this part is correct *AND* your math is right, but you weren't supposed to get it that way" I ended up getting only half credit for that problem This was an assignment where we had to do ten problems but only *two* of them would be selected at random and graded so one quarter of my grade on that went out the window Needless to say, I was salty

Deanna Baxter if the students are interested in this integral in the first place, they should be ok and understanding this shorthand notation. Btw, a MIT professor also does that in his calc lectures for improper integral.

Here kzfaq.info/get/bejne/gc6nhK52xNrQlGQ.html

Thanks for the comment and thanks for watching!! :)

He is using the limit as x -> 0 of sin(x)/x which equals 1.

the function is undefined, but the derivative isn't

I(b) is defined in 0 but I'(b) isn't defined in 0

For example the function f(x)=sqrt(x) is defined in 0 but its derivate is not defined in 0 because f'(x)= 1/(2*sqrt(x))

Thanks Donny. You can also check out Zach's page in my description. He has a lot of great stuff there!

thomas g Just got to it, I reckon he's solved it already, then started talking about his steps and realised it'd fit better with the part where he was previously (in his timeline) talking about it.

It's so he can outline that b has to be positive, and it probably makes the most sense to put the clip here

When u sleep on class

it spoiled the rest of the video

To be fair, Zach showed me (as I mentioned in the video).

伊藤那由多 loll

AugustoDRA thank you!

⁠@@blackpenredpen what’s the concept of this Feynman’s method? I studied calculus but I don’t think I’ve seen this method and I wasn’t taught this. How do I know when to use and for what integrals? Please, I’m trying to understand it. I’m studying A-level maths in the Uk, if that’s helpful. Thank you 😁 also I love your videos! So good

x approaches 0 from the right. With a weapon. Also discussed later in the comments