"Reverse" Riemann Sums | Finding the Definite Integral Given a Sum

[@jayden7194]

100% the best example video i found online.... been struggling with this topic for hours and this video is very clear. thank you so much.

[@md.mozibur.rahman]

I watched a coupe of videos over this topic, and this video was so understandable because of those examples. Thanks a lot.

[@nonentity168]

Thanks, professor. I've been struggling with finding the function formula, and this algorithm clears it up.

[@rockyjoe3817]

Among all of the people that I saw on youtube you have the best explanation on integerals :D

[@naiko1744]

Idk why this confused me so much at first, but basically what we are doing is going from the integral definition to the integral notation. We have to be careful because the actual function, the length of each rectangle's base, and the x point at which we evaluate the height of each rectangle are all jumbled together! Therefore we rewrite the expression, clearly identifying each part, and then we can easily get to the integral notation! :)

[@johanmattlin2138]

Why does xi n divided by 3 become 3 divided by xi n ?

[@mohammadfahrurrozy8082]

@@bluehouse41i know im late for a month or so. the "dx" part? no. it is from 1/i from the original sum. he change the "i" to be (xi/3)n in blue marker.. since in the first sum its 1/i, then it become 3/(xi . n) hope it helps

[@neeldeshmukh3705]

If education was like this in India we may be developed not developing. Good Tut's btw. Better than my college maam

[@rockyjoe3817]

Lol don't say that , you Indians have one of the best education in the world !!! I am not being sarcastic.

[@AdityaKrishnan17293621_Osaka]

In my personal opinion and experience (as an Indian student), I have met very few people who learn for the fun of it. Most people learn for marks, it seems. I used to be a very curious guy (and would still love to be) but I too have sadly started learning a lot of stuff blindly. Not stopping to wonder as often as I used to. I really hope this changes soon

[@nishantbhat260]

@@AdityaKrishnan17293621_Osaka I hope this changes with our new education policy this year.

[@AdityaKrishnan17293621_Osaka]

@@nishantbhat260 cheers to that! :)

[@jamesdesantis9420]

It seems to me that the first sum should be [2,5], not [0,3]. Since you have 2 +3i/n in the sum, that corresponds to a + (delta x)i where a = 2 and (deltax)i is 3i/n, which would make b= 5 (since 5 - 3 - 2). Also, if you let i go to n, then 2 + 3i/n becomes 2 + 3n/n = 2 + 3 = 5.

[@kennethreed7744]

how do you do this if you're not given the explicit interval in the beginning? if not given, how do you find your a and b values with your technique?

[@calvind7519]

why is the answer tan(2+x)? f(x)= a+ delta x therefore shouldnt the answer be tan(x) instead?

[@aashsyed1277]

hi great videos! Trefor! You are doing a great job! but why is there a private video inthe calc 1 playlist?

[@DrTrefor]

Oops fixed.

[@aashsyed1277]

@@DrTrefor what video was it?

[@pokoknyaakuimut001]

Thank you very much

[@TruthOfZ0]

What if it didnt have the i?

[@naiko1744]

If you don't have i and the summation is not using another letter instead of i, and if you cannot get it from i = (xi * n / interval-size) then... you just don't have an integral there! haha

[@TruthOfZ0]

@@naiko1744 i, is a counter step number of the steps on a summation function, yes it could be any symbol.....it is weirdly potitioned where it makes solvable the transition from sumation to integral and vise versa....if it isnt there or it is located weirdly in the function making things more complicated...it doesnt seem to work .. Anyway my reasoning was to make an integral or a summation that doesnt have the i in it..to make it have it on purpose....so we can turn an unsolvable integral into a solvable summation and vise versa ... kinda lika Umbral Calculus but not same!

[@Sisyphussa01]

Damn, it got really from 0 to 100 in the past couple of videos...

[@chiomai5173]

God bless you

[@thomasacuna6773]

Why does xi n divided by 3 become 3 divided by xi n ?