Real Analysis 60 | Integrals on Unbounded Domains

[@mastershooter64]

another awesome video!

[@Hold_it]

If this goes on, then i will not be able to do math without hearing your voice :)
Not that i am complaining.

[@brightsideofmaths]

Great :D

[@jonasw4791]

nice video!

[@scollyer.tuition]

Shouldn't you have mentioned questions of convergence and Cauchy principal value, and so on? Or will you be dealing with that later?

[@brightsideofmaths]

Cauchy principle value is something for Complex Analysis :)

[@scollyer.tuition]

@@brightsideofmaths Hmm. I have more than one real analysis text that defines CPV for both unbounded integrals, and bounded integrals with a singularity in the interior of the domain of integration. e.g.
int_\infty^\infty f(x) dx = lim_{R \to \infty}
\int_R^R f(x) dx
Are we talking about the same thing?

[@brightsideofmaths]

@@scollyer.tuition You are totally right. The topic of CPV is fitting for a real analysis course. However, I decided to cover this, more generally, in my Complex Analysis course. Simply because I have the option. If you find that too strange, I can do another video in the Real Analysis series as well.

[@scollyer.tuition]

@@brightsideofmaths No, it's entirely up to you, of course. And sometimes the correct place to explain things isn't entirely clear. (I think generally that it's a good idea to cover topics more than once, maybe from different points of view)
I feel that it may be appropriate to mention it here though, else someone may draw the conclusion that the treatment of the limits in an unbounded real integral is not particularly important.

[@evionlast]

So close to double integration ... 🤔 yet so far...

[@jeandetti6250]

First one to like this tweet

[@brightsideofmaths]

It's a video :)

[@mastershooter64]

@@brightsideofmaths a video is homomorphic to a tweet :D

[@lolygagger5991]

@@mastershooter64 nice