Finding integral from Riemann Sum

In this video, I showed how to relate a Riemann Sum to a definite integral

[jumpman]

When writing the limit as an integral, I noticed that 𝑓(𝑥) = 𝑥² − 1 _almost_ works, so I guessed that it was really 𝑓(𝑥) = 𝑘𝑥² − 1 for some constant 𝑘.
Plugging that into the Riemann sum I found that 𝑘 = 4 works, and that gave me the boundaries 𝑎 = 1 ∕ 2 and 𝑏 = 5 ∕ 2.
So my integral became ∫[1 ∕ 2, 5 ∕ 2] (4𝑥² − 1)𝑑𝑥, which also happens to evaluate to 56 ∕ 3.
Great video by the way!

[syamantagogoi]

Dear Sir, I really appreciated the way you have articulated it. Things have become easily comprehandable for me with full of clarity.I resolved these problems myself in my note pad with full of confidence having watched this video. Thanks a lot and keep on enlightening the viewers like us.

[lastchance]

Great explanation. Appreciate that you expanded the problem to include finding and evaluating the integral. This allowed us to gain more insight into the meaning of the terms. Brilliant!

[hasandogan]

Bro you deserve a lot more than this! Keep going on!

[skwbusaidi]

The integeral that I have reach to is
1/2 integeral of x^2-1 from 1 to 5
Which give the same value of 56/3

This can be reach be letting delta x = 4/n and a=1and b=5

[jan-willemreens]

... Good day Newton, When I watch a presentation of this topic, the problem for me is not to be able to follow it properly, but to possibly reproduce it! In short I don't find this subject difficult, but it still is difficult to give the whole material a firm place in my head, isn't it crazy?! A subject that I therefore have to repeat regularly, to be able to explain it to other interested students over and over again! Newton, thank you for another clear presentation on Riemann, and I will also recommend it to other students having some problems regarding this topic; great work! Take care, Jan-W

[SonuKumar-swcr]

Awesome explanation... Seems quite doable

[steveinstpaul]

Excellent explanation. Thanks. I look forward to watching more of your videos.

[michellauzon]

Lim = 2 * Integral ((1 + 4x) ** 2 dx) (from 0 to 1) - 2.

[sevenser]

Happy New year :)
Nice to watch your video today

[beez]

I am confused by how he got 2n^3+3n^2+n when he expanded n(n+1)(n+1), because it looks like it should be n(n^2+2n+1) => n^3+2n^2+n, could someone explain please?

[cameronspalding]

For this part I would use Oh notation rather than write out the full fraction.

[cameronspalding]

When I saw this I kept treating i like it was the imaginary unit, so I thought it would involve a contour integral!

[bobbyno]

haha 8:45 "lorem ipsum dolor sit amet, consectetur adipiscing elit. Vivamus auctor id justor eu ultrices" means customer service with a basketball coach.