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Thread: Riemann Sums, Sparknotes version.

  1. #1
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    Riemann Sums, Sparknotes version.

    Ok, I am aware of how to do (not fluently) summations, but Riemann sums throw me off so much. So here is my best description:

    $\displaystyle n$
    $\displaystyle \sum$$\displaystyle k^2$
    $\displaystyle i=1$
    This turns to :
    $\displaystyle n$
    $\displaystyle \sum$$\displaystyle f(i)$
    $\displaystyle i=1$
    Where $\displaystyle f(i)=i^2$.

    Ok, I know $\displaystyle n$ is the number of "rectangles" which will approach infinity. Your counter is $\displaystyle i$, which replaces $\displaystyle k$ or $\displaystyle x$ or whatever you use. How do I find $\displaystyle c$, and where does $\displaystyle \Delta x$ come from? What do they mean? What is the difference between regular sums and Riemann sums? I am pretty quick to follow along, so feel free to be brief, I should be able to keep up. I also know most of the $\displaystyle i \Rightarrow n$ conversions, e.g. $\displaystyle c=cn$, $\displaystyle i^2= \frac {n(n+1)(2n+1)}{6}$ or whatever, I just need to figure out $\displaystyle ci$ and $\displaystyle \Delta x$. I also have trouble figuring out riemann summations in general, a quick drive by of HOW to do them would be great, I already know why they work, I just can't make them work.
    Last edited by Thikr; May 4th 2010 at 06:59 PM.
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  2. #2
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    Joined
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    How to Find Approximate Area Using Sigma Notation Video ? 5min.com

    Areas, Riemann Sums, and Definite Integrals Video ? 5min.com

    Calculus Videos
    (video's 21 to 23!)

    YouTube - Calculating a Definite Integral Using Riemann Sums - Part 1
    (and part two!).

    I think if you watch these videos in order you'll ace Riemann sums & understand everything perfectly.

    By the way, the sum you've shown is not a Riemann sum but it is a summation formula.

    There is a way to derive it but I suggest to you to first concentrate on understanding a Riemann sum & what it is then come back to tis forum to ask how to derive this formula.
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