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.
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.
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.
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.
yes, this is amazing ... stay curious
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.
agree, this is awesome ... stay curious
Excellent lecture. The last example is very interesting and clarifying the backward substitution rule.
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.
Indeed :)
💕💕💕💕💕 awesome, solving integrals is so much fun 💕💕💕💕💕
thank you for these lectures !!
you are very welcome! And thanks for the support :)
Sir how can you shift dt to RHS
It is not independent
I don't really understand your question. Can you explain more?
great video,☝
Glad you enjoyed it :)
好
12:53 - if the upper limit is 10, we just can take ϕ(t) = sin(t/10) and call it a day?
10 would be a problem here since the function is not defined at 1.