Real Analysis 57 | Integration by Substitution

📝 Find more here: tbsom.de/s/ra
👍 Support the channel on Steady: steadyhq.com/e...
Other possibilities here: tbsom.de/sp
You can also support me via PayPal: paypal.me/brig...
Or via Ko-fi: ko-fi.com/theb...
Or via Patreon: / bsom
Or via other methods: thebrightsideo...
Join this channel on UA-cam: / @brightsideofmaths
💬 Access to the community forum: thebrightsideo...
🕚 Early access for videos: thebrightsideo...
❓ FAQ: thebrightsideo...
🛠️ What tools do you use: thebrightsideo...
📚 Download my books: thebrightsideo...
🆓 Ad-free access to all videos: thebrightsideo...
Please consider to support me if this video was helpful such that I can continue to produce them :)
Each supporter gets access to the additional material. If you need more information, just send me an email: tbsom.de/s/mail
Watch the whole video series about Real Analysis and download PDF versions, quizzes and exercises: tbsom.de/s/ra
Supporting me via Steady is the best option for me and you. Please consider choosing a supporter package here: tbsom.de/s/sub...
🌙 There is also a dark mode version of this video: • Real Analysis 57 | Int...
🔆 There is also a bright mode version of this video: • Real Analysis 57 | Int...
🔆 To find the UA-cam-Playlist, click here for the bright version: • Real Analysis
🌙 And click here for the dark version of the playlist: • Real Analysis [dark ve...
🙏 Thanks to all supporters! They are mentioned in the credits of the video :)
This is my video series about Real Analysis. We talk about sequences, series, continuous functions, differentiable functions, and integral. I hope that it will help everyone who wants to learn about it.
x
#RealAnalysis
#Mathematics
#Calculus
#LearnMath
#Integrals
#Derivatives
#Studying
I hope that this helps students, pupils and others. Have fun!
(This explanation fits to lectures for students in their first and second year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)
For questions, you can contact me: steadyhq.com/e...

[@scollyer.tuition]

This is a very nicely structured lecture. And I'm glad to see someone cleanly explaining the requirement for bijectivity - this is very often omitted, or poorly explained.

[@FraserIland]

Congratulations!
This is by far the highest quality lecture about Integration by Substitution which I have ever seen from a teacher or a book. Well done indeed.

[@sinanakhostin6604]

Excellent lecture. The last example is very interesting and clarifying the backward substitution rule.

[@japedr]

13:35 just a quick clarification. In general, the denominator would be equal to |cos t|, as we are taking the positive square root. But in the region of integration it is nonnegative, so the simplification is correct here.

[@brightsideofmaths]

Indeed :)

[@kz1662]

thank you for these lectures !!

[@brightsideofmaths]

you are very welcome! And thanks for the support :)

[@matejzadny8421]

great video,☝

[@brightsideofmaths]

Glad you enjoyed it :)

[@sureacademykaklk6038]

Sir how can you shift dt to RHS
It is not independent

[@brightsideofmaths]

I don't really understand your question. Can you explain more?

[@tsunningwah3471]

好

[@PrzemyslawSliwinski]

12:53 - if the upper limit is 10, we just can take ϕ(t) = sin(t/10) and call it a day?

[@brightsideofmaths]

10 would be a problem here since the function is not defined at 1.