Real Analysis 57 | Integration by Substitution

[@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.

[@silentintegrals9104]

yes, this is amazing ... stay curious

[@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.

[@silentintegrals9104]

agree, this is awesome ... stay curious

[@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 :)

[@silentintegrals9104]

💕💕💕💕💕 awesome, solving integrals is so much fun 💕💕💕💕💕

[@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.