Solving Integral: ∫ sin x / x dx

❓Solving Integral: ∫ sin x / x dx
🔍 Welcome to my channel, if it is your first time I would highly encourage you to check out my channel (link below).
Go to my channel: 👉 www.youtube.com/@mohammadsena...
My Integral Playlist: 👉 • Solving Integrals: The...
🖌️ Visual Learning: Visualize mathematical concepts through animated illustrations, providing a dynamic understanding of integral solutions.
💻 Powered by Python: Every aspect, from solving integrals to video editing and animations, is meticulously crafted using the power of Python.
🎶 Peaceful Background Music: Enjoy the rhythm of random, peaceful melodies as we delve into the world of integrals.
🔍 Reasoning Through Each Step: Dive deep into the logic behind every integral solution, empowering you to comprehend and replicate the process.
🎓 Student-Friendly Approach: Tailored for students, this channel offers clear and no-nonsense solutions to various mathematical challenges.
Join me on this problem-solving journey, where every solution is a step towards mastering the art of mathematics.
Don't forget to LIKE 👍, SHARE 🔗, and SUBSCRIBE ❤️‍🔥 to make math integral popular and support this channel! 🌐🧮
#computerscienceengineering #computerscience #mathematics #python #problemsolving
#education #mathjourney #studentlife #mathisfun #learningadventures #mathconcepts
#visuallearning #studyinspiration #studentcommunity #mathchallenge #techineducation
#interactivelearning #studymotivation #mathematicsforall

[@darcash1738]

Nice. Also, Feynman works for the definite bounded one 👍

[@mohammadsenanali]

Good to know!

[@lavonoff]

You forgot to add +C :)

[@jamilshirinov2931]

What program did you for the creation of this video? The animations are just next level!

[@mohammadsenanali]

I created this with the help of Python. 🐍

[@rhumannpurple4]

this is called MANIM created by 3Blue1Brown

Muy buen video Genio!

[@danielc.martin1574]

Que narices? 😂

[@user-he3bx5ds7u]

+C

[@aadityakiran07]

cool. looks just like 3b1b

[@SRINIX4356]

next time, dont forget a constant +C

[@mohammadsenanali]

Sure

[@itachu.]

by parts?

[@antoine35210]

does it work ?

[@jacobstarr9010]

No, if you try it the values of 1/x will just infinitely decrease and the values of sinx will just cycle between sinx and cosx indefinitely. Since you can’t get back to the original function, integration by parts won’t work. Also, the integral is non-elementary which is why the creator used a maclaurin series to “evaluate” it.

[@antoine35210]

@@jacobstarr9010 yeah i was confused bcs my man up there said he did it by parts

[@bjornfeuerbacher5514]

Don't you have to prove that this power series actually converges?

[@user-ze7jv1vw4b]

I also want to know

[@phylI]

It converges with Leibniz

[@jacobstarr9010]

No, it is an indefinite integral so we don’t need to prove it. Also, the Maclaurin series of sinx converges for all real numbers, so it will converge regardless of the values.

[@bjornfeuerbacher5514]

@@jacobstarr9010 What does my question have to do with this being an indefinite integral? And how does "the integral of the series converges" follow from "the series itself converges"?

[@jacobstarr9010]

@@bjornfeuerbacher5514 well, sinx converges for all x. And all we change is the removal of 1 power of x. This doesn’t change much, since x^-1 is a polynomial and not a series. So we can assume the same. In fact, if we want to prove it, we can use the ratio test. By using the ratio test, we find the limit to be equal to zero, and zero times x^2 will be zero for all x. That means no matter what value of x we use, the integral will converge. And the reason I say it doesn’t matter for an indefinite integral is because we treat x as a variable. If we were to say we want to evaluate the integral from 0 to 1, then convergence would matter because we would want to verify that these x values are within the interval of convergence. But since the radius of convergence is infinity, the x values will converge for all x. So in summary, it doesn’t matter unless we have values of x we want to plug in.

[@Agentsecret]

0:25 why ? justifies

[@mohammadsenanali]

The integration of a sum is equal to the sum of the integrations. Cheers!

[@xninja2369]

@@mohammadsenanali that took me a while to understand 😂

[@castagnos509]

that's not allways the case for infinite sums

[@antoine35210]

just bcs integral is linear and so is sigma

[@danielc.martin1574]

This is not elementary 😮😂

[@mohammadsenanali]

Exactly

[@filipeoliveira7001]

You learn this in AP Calculus BC though

[@danielc.martin1574]

@@filipeoliveira7001 do you prove it?

[@filipeoliveira7001]

@@danielc.martin1574 You learn the tools to prove it: Taylor Expanion (Mclaurin representation of sin(x)), Summation Integration, and how to determine convergence of an integral and of a power series.