Wow! My calculus professor never explained why the integral test works (even when I asked her directly), she just described the conditions under which the integral test can be used. Dr. Bazett, your explanation is so clear and well explained. Thank you for finally giving me the explanation that I've been searching for.
This is the first example, anywhere, that has mentioned that the “dx” here is 1. Every other video and textbook seemed to assume the student would understand that, but because you emphasized it, I can finally understand the integral test conceptually.
I am really grateful for your detailed explanation and patience in explaining this point. I finally understand it after struggling to understand it by myself for so many days. Thank you so much! :-)
You are correct, but so is the video. If the improper integral converges, then the sum from 2 to infinity converges, which is equivalent to saying the sum from 1 to infinity converges, since the first term does not affect convergence :)
@Dr.Trefore Bazette I am bit late.Can you explain why the "less than or equal" sign used in the statement where the inegral is less than summation of a sub n?
@@DrTrefor Thanks for reply. Do you mean we can also apply integral test for increasing function or not? I am sorry I am still confused because I think the same inequalities are obtained for increasing function and same comparison can be used for increasing functions as well. However I think in case of increasing functions, other tests (like n-th term test ) are better to use. Am I right? Sir if possible for you, please make a video on this or otherwise please elaborate it in detail. I will be grateful. Regards.
@@DrTrefor I agree that f needs to be continuous (otherwise it may be undefined at integers in the first place). I also agree that it needs to be monotonic (eg: the test doesn't work on f=sin^2(pi*x)). What my doubt is that if the test works for f being positive AND monotonically decreasing, shouldn't it work for positive AND monotonically increasing as well?
49 seconds into the video and this makes so much more sense than trying to learn elsewhere 🙌
Wow! My calculus professor never explained why the integral test works (even when I asked her directly), she just described the conditions under which the integral test can be used. Dr. Bazett, your explanation is so clear and well explained. Thank you for finally giving me the explanation that I've been searching for.
This is the first example, anywhere, that has mentioned that the “dx” here is 1. Every other video and textbook seemed to assume the student would understand that, but because you emphasized it, I can finally understand the integral test conceptually.
Your videos are a gift, thank you. I find them a lot more clear/concise than many more popular channels, and especially moreso than my textbook.
One of the best math channels when it comes to building intuition behind calculus
I am really grateful for your detailed explanation and patience in explaining this point. I finally understand it after struggling to understand it by myself for so many days. Thank you so much! :-)
You explained this very well. Thank you Mr Bazzett!
Superb content as always. Calculus looks intuitive with your series! Very well done proffesor. 🎉
me sorprende que no tenga más vistas, está buenísimo
Very well explained professor!
Your videos are very well made. Thank you for the explanation, I was having trouble understanding the concept only by the textbook
Very helpful, thanks
Great video! Thank you so much.
Absolutely amazing! Thank you so much!
You're very welcome!
great video thanks
Hi thank you for the awesome contents!what software do you use to create the visuals?
Thank you so much professor. CLEAR!!!!!
Спасибо большое за большую работу...
6:52 I think it should be sum from n=2 for convergence test
You are correct, but so is the video. If the improper integral converges, then the sum from 2 to infinity converges, which is equivalent to saying the sum from 1 to infinity converges, since the first term does not affect convergence :)
Thank u sir for such a intuitive , clear and well animated explanation
Sir plz make video on logarthmic and raabe's test and what is the intuition behind them
this episode is god like!
Great explanation!
@Dr.Trefore Bazette I am bit late.Can you explain why the "less than or equal" sign used in the statement where the inegral is less than summation of a sub n?
thank u sooooo much!!!! really helpful
Shoutout Prof. Allen
the best
Thank you so much Sir
We can use this as a test both ways
Right ?
great sir btw can you tell me which app you used for these math animatios?like in 1:40
I use MATLAB
Couldn't you use the rectangles from the first example on always increasing functions to prove they converge
Sir @Dr. Trefor Bazett, why we can't apply integral test when the function f(x) is increasing?
It would be saying it was smaller than something divergent, which means it could be divergent or convergent.
@@DrTrefor Thanks for reply. Do you mean we can also apply integral test for increasing function or not? I am sorry I am still confused because I think the same inequalities are obtained for increasing function and same comparison can be used for increasing functions as well. However I think in case of increasing functions, other tests (like n-th term test ) are better to use. Am I right?
Sir if possible for you, please make a video on this or otherwise please elaborate it in detail.
I will be grateful.
Regards.
Thank you!
why the n here in (1) is not n=2?
Why does f need to be positive, continuous, and monotonically decreasing?
@@DrTrefor I agree that f needs to be continuous (otherwise it may be undefined at integers in the first place). I also agree that it needs to be monotonic (eg: the test doesn't work on f=sin^2(pi*x)).
What my doubt is that if the test works for f being positive AND monotonically decreasing, shouldn't it work for positive AND monotonically increasing as well?
@@avneeshkhanna I have the same question too. Maybe you understand more about math and could help me understand it? thank you
got a test coming up, betting all my cards on this series cuz i sure as hell aint betting it on my brain
Good luck!!
Marksman says good luck too.
Sir! Doesn't this test give us the exact value to which the series converge?
No
Nope. Just tell you whether convergence or not. Important Note : The number to which integral converges is not the sum of there series!
Very well explained!!