Real Analysis 54 | First Fundamental Theorem of Calculus

[@davidzhang8764]

The timing of this is so perfect. I can't believe there are videos on this as I'm learning it in university!

[@brightsideofmaths]

Thanks :)

[@Phyyzix]

Hi I recently became a supporter because this series is just so good. Will there be more exercises available for other parts in the series? Again, thanks for your time doing this!

[@mastershooter64]

you can just get exercises from a real analysis book

[@sinanakhostin6604]

There is something in the last example (probably very rudimentary) that confuses me. Unlike the example in lesson 52 (where you demonstrated the calculation of sum of rectangles from bellow and above) where you started from index 1, here you started the sum from a=0 and until n-1. why?!

[@brightsideofmaths]

There is no particular reason. Here I just wanted to avoid (k-1), but of course, it works the same when starting from the index 1. In the end, it is just important, that you sum up all rectangles correctly, no matter which arbitrarily chosen indices you use.

[@edztyMKWII]

could you tell me what software you use to make these notes? Seems very handy.

[@brightsideofmaths]

Yes, I can definitely tell you :)

[@edztyMKWII]

@@brightsideofmaths 🤣 ok what is it

[@brightsideofmaths]

Xournal :)

[@hyperduality2838]

Integration (syntropy) is dual to differentiation (entropy). Derivatives are dual to anti-derivatives.

[@mnada72]

First of all Thank you for the nice topics. I am confused by the name antiderivative , is it the integral function or the derivative of the integral function ?

[@brightsideofmaths]

It is the integral of function f from a to x.

[@anjanbhattacharjeesir]

Great ❤❤❤🎉

[@scollyer.tuition]

Bin ich der erste? Toll!!!