You bring up a good point. Generally, the answer to an integral should have a +C, but the point I was trying to demonstrate was that e^x is its own derivative and can be its own antiderivative. In the video, we are primarily interested with the area under the curve, which is e^x. However, it is true that the derivative of the function of the form e^x +C is e^x.

@@COOLGOLU Thank you!!

@ Thank you!

Yes, I've studdied complex analysis and analytic number theory for 5 years and in complex analysis you come across infinity quite alot. Well not in the same way shown in this video but rather singularities of a function. In fact if my momeory serves me right there is a theorem that states that every function can be expressed using its discontinuities but there is no neat formula for it. Also a conjecture I've been working on a proof for about 2 months now states that any analytic function f can be expressed as the sum of the singularities of the mellin transform of f times a first order root. Hence any analytic function f's mellin transform must have first order singularities so the first order singularities and first order roots terminates. I would also recommend watching some videos on the gödstein sequence where you use infinite ordinals to prove it always terminates

@@siddude8021 Right, but do you see infinity in real life? By that, I mean do you use infinity to explain or analyze real PHYSICAL things, not abstract concept?

@magnetospin well that's the thing, many of these theorems have real applications and although they might not be useful for the average Joe most of mathematics is not useful and made useful by engineers and physicists. Basically if maths is a language then understanding the language and its boundaries better helps us better understand how to apply this language to describe the world around us

@magnetospin I think a good example is the potential energy of a body within the gravitational force of another object. Then you imagine that you have 0 potential energy when you are at some point infinitely far away from the object. Basically F = G * m*M/r^2 then the potential energy = integral from inf to R of F dr = - G*M*m/r

@@siddude8021 See, this is the issue I am talking about. No human(or object) is infinitely far away from another object, within the casually linked space anyway, so does this still have any application?

That's something that's also amazed me. Startalk has an very insightful video that explains just this. What makes it even more exciting is that the fractal constructing any measured surface can be a decimal dimension!

I am from Romania and it recommended me also

@@channaduminda5072 It means a lot to me!

I’m not 🙂

Wow, I wish you all the best! And don't worry, I'm sure you'll pass with flying colours :)

@@pentagon-math Hmmm, i hope so. And i will thanks u if i get good marks tomorrow or i will thank u any way for the 'Flying colours wishes hahah'

Hi 🙂. Guess what I am "Fail" and I proved my AXIOMS. 🥲🥲

Thank you very much! I appreciate the kind words.

Thank you!!!

Thank you for the subscription & for the comment

I really appreciate your kind words and I wish you the best of luck!

Thanks for the comment, I am working on a couple of good problems, will be uploading soon

You are most welcome

Thanks! 😃

Thank you