Are These All of the Types of Integrals?

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[s.rehman.]

This is one of those videos that make maths look hard and scare students away from maths. Instead of telling people supposedly the "types of integrals", tell them it's the same basic idea but it is profoundly useful in many ways (your "type of integrals").

[Frdnnd]

I'm 20 and haven't even finished* algebra yet; I'm not sure if i belong here, but your channel is somehow still captivating to an amateur like me.

[aangulog]

Although knowing these concepts and where to use them is really useful, I wouldn't categorize them as "types of integrals", some where legit different definitions of integral, but most of them where just famous/useful applications/transformations dealing with Lebesgue integrals.

And since the Lebesgue integral is one of the most important ones talking more in depth about it would be really cool, specially the theorems of representation which indeed confirms that the Lebesgue integral is the correct generalization of the Riemann Integral

[fdileo]

I knew around 21/22 of them. I'm looking forward to watching the Riemann-Stieltjes integral video

[mdperpe]

I would add product integral, where the "small pieces" usually have values close to unity instead of zero, and are multiplied instead of summed.
For ordinary numbers, we have P∫ f(x)^dx = exp (∫ ln f(x) dx), but when the function takes values in a non-commutative algebraic structure (e.g. a group), then things become more interesting. The solution of a time-dependent Schrödinger equation can be written as a product integral.

[daxplatiro]

What about the Mcshane Integral? I love it as it can be thought of as Generalizing the Gauge Integral in a way, and relating to the Lebegue integral in a way unifying the theory of integration. This is not the best explanation but you should check it out!

[rick]

Also on a separate note here… the Ito integral is a member of a broad class of stochastic integrals.

There many more stochastic integrals, Ito is the most common thats rises naturally when building stochastic DE.



Looking forward to your take on RS integral. There’s a nice paper from 1989 going about geometry behind RS integral.


Essentially you end up calculating areas of projected fx over the weight function induced by g(x) and its derivative.

After that sums and integral fused in a single object on my head. 😅

[jammasound]

Nice overview, I'm still learning on the Riemann integral 😃

[mahmoudhabib]

Please make a video about the Bochner integral! I've come across it during research and I need to better understand it. Thanks a lot. 💖

[maxvangulik]

not sure if the 3 types of product integral have geometric interpretations, but I didn't see them on the list either way

[hazimahmed]

What is the difference between a surface integral and a double integral? Same doubt I have for volume integral and triple integral.

[rick]

This video is awesome!!! Didn’t knew s couple here… check the product integral.

Quick application: survival analysis for estimating the survival function. A data driven analog is related to the kaplan meier estimator of survival function of a non negative random variable

[InputOutput-bl]

Cam you do a video about the feyman integral??

[filipnagy]

what about integral of forms on a manifold?

[OpPhilo]

Love from india sir and mam.
1st time i have watch your video on Group theory which is Galois theory. I impressed you and mam.
Thank you for giving us valuable information.

[SobTim-euxu]

Yay, new video)
And like I know 12/33

[sphakamisozondi]

I never knew there are different types of intergrals. I thought there were two, 😅

[Satisfiyingvideo-uupw]

is there any formula for pi product. Like i want to multiply .is there for sequence like an+b here a and b is constant