Riemann sum, finite sum, integration part 2

www.midnighttutor.com Check out the whole collection of tutorials. Tutorial on how to calculate a riemann sum and take the limit to arrive at the integral

Category:

Howto & Style

Tags:

• calculus
• riemann
• sum
• integration

[cms271828]

I think it would have been clearer to take the height from the right side of each strip, since going from left side and including the n'th strip means you go outside of the area your looking at(Doesn't matter in the end, since its just one strip whose area tends to 0).

I think using A(n)=SUM[i=1 to n]{f(ix/n)*(x/n)} where n is number of strips is neater.

[midnighttutor]

You are sort of correct. I ended up using exactly the formulation you wrote out except I also included the i=0 contribution which happens to be zero.

[nj427s]

I still dont get the part where he substituted the infinite sum of k2 to k(k+1)(k+2) ect....

[midnighttutor]

Youtube cropped the video. Go to midnighttutor dot com to see the full field of view (and higher resolution) version of the same video....also free.

[FlippinPin0y]

you explain this very well and I appreciate what you have done for students =)

[ironclownfish]

That thing on the back of his shirt looks like a diagonal butt

[krishields]

@krishields

Unfortunately, mathematical definitions are not sufficiently equipped to actually handle what I would refer to as true limits, for we would have to accept the actual distance between any two n is zero. Therefore, under current definitions, we would be forced to conclude the area is zero. 

[krishields]

There is a logical contradiction I see with limits - which you actually expressed. When n is taken to the limit, the value of the second part, 3/n goes to zero and the value of the third, 1/n^2 goes to zero "even faster" - which is true. Yet, both are *somehow* supposed to "reach" zero at the same time. If the third reaches the limit, zero, before the second then we are forced to concede that n was not taken to the limit.

[Quacyify]

cool!!!!!

[roopu8]

great

[wastedbrains13]

Thanks, I'm Mexican and I don't speak english very good. But also this video was so usefully to understand the riemann sum, because the explanations in spanish are very bad. Thanks. The math language it's universal.

[romyboy]

that a good lesson now i know where the formula from integrating a polynomial came from.

[Claudio5205]

Muchas Gracias

[yonatanalemayehu]

Wonderful lecture...

[Hammama]

U R THE MAAAAAN!!!

[qstong]

thank you very much. it saved me great deal of time comparing to read the tedious textbook.