Definite Integrals Defined w. Riemann Limit of Sums Example Calculus 1 AB

[profrobbob]

No..."you da best" for sending such a nice comment! I'm so glad I could help to complete the missing portions of your calculus lessons...you know, you were the one who took the time and initiative to find my videos...I say to that "GREAT JOB"! I hope I can continue to be your go-to video channel..and please be sure to share with your friends too...thanks:)

[UrielD]

Thank you for the video Prof. At 2:32 you said: "it's just fancier notation" instead of writing as n approaches infinity as we did in previous examples; and after thinking about it i realized that it is important to make that distinction, because if the widths of the partitions are not equal then saying the limit as n approaches infinity not necessarily will give me the exact area under the function. You can have the number of partitions approach infinity (denoted by as n approaches infinity in the limit of course) and the magnitude of the norm could well be infinitely close to the value of (b minus a) and hence the computation results in a very "off" estimation of the actual area under the function (it will be almost like computing the area with one partition). Now, If the widths of the partitions are all equal, as would be in most cases (i guess) then as n approaches infinity, the norm approaches 0 invariably and the computation will produce the exact area under the function which we are looking for ultimately. So denoting in the definition that the magnitude of the norm approaches 0 instead of writing as n approaches infinity will guarantee that we always are computing the infinitely actual area under the function. Anyways i hope it was helpful, and as always thank you Mr. Tarrou!

[badguyfromstarwars]

I love the chandelier! Adding some extravagance to the 'class room', well done! Oh, right, I also wanna tell you that your videos are awesome! I'm  binge-watching these for an upcoming exam and it's actually pretty pleasant. Soothing. Not like sitting with your nose in these dry books and just go by 'trail and error'. Keep up the good work!

[zackisser]

You are a good teacher, thanx for the great work Bam ...

[matthewreed]

So I'm a little confused. In the first step in solving the limit, where does the "n" in the numerator of the first term come from? Why would you not leave it just as 2+(2i/n)?

[senthuy]

For the example you showed how do yu calcuate the "ci" for the f(ci)? What does the ci even mean?

[nitti]

In your A= equation on the left side, should the deltaX have an i?

[MrGittle]

why when you use the evaluation theorem does it not come out to be 56?

[zeeveezeevee]

I can't find an example of a definite integral defined as a Riemanns sum with an infinite amount of subintervals and left endpoints. Have you made one?

[Garrtt]

Holy calculus! Go back to the old board with the class room please! I have learned from a ton of your videos from that classroom! New is :)

[Jabermania]

1:20 but why is it integral? it should be derivative right

[Truth]

I love your videos and thank you for them, but the 90's wants its shirt back.

[jamieoliversmum]

Hi sir,

You are one great professor and Im thankful for all everything you've done. I have a suggestion if you may. I think you should make an organized series on integrals. You have too many videos on integrals and I cant seem to find my starting point and my finish point.

All the best,

Jamie Olivers Mum