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Math Help - Riemann Sums

  1. #1
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    Riemann Sums

    How can I estimate the areas of the left and right side for Riemann Sums??! This is really confusing me.

    For example  f(x) = 5/x
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  2. #2
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    Quote Originally Posted by skyslimit View Post
    How can I estimate the areas of the left and right side for Riemann Sums??! For example  f(x) = 5/x
    Over what interval?
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by skyslimit View Post
    How can I estimate the areas of the left and right side for Riemann Sums??! This is really confusing me.

    For example  f(x) = 5/x
    You have no interval, so I will do it for the interval [a,b]. So we would have that \Delta{x}=\frac{b-a}{n}, where that is n partitions of the region. We would also have that f\left(a+\Delta{x}i\right)=f\left(a+\frac{b-a}{n}i\right)=\frac{5}{a+\frac{b-a}{n}i}. So we would have that \int_a^{b}\frac{5}{x}dx\approx\sum_{i=1}^{n}\frac{  5}{a+\frac{b-a}{n}i}\cdot\frac{b-a}{n} and that \int_a^b\frac{5}{x}dx=\lim_{n\to\infty}\sum_{i=1}^  {n}\frac{5}{a+\frac{b-a}{n}i}\cdot\frac{b-a}{n}.

    To illustrate the point \int_1^{e}\frac{5}{x}dx=5 and \left|\int_1^{e}\frac{5}{x}dx-\sum_{i=1}^{500}\frac{5}{1+\frac{e-1}{500}i}\cdot\frac{e-1}{500}\right|<.006
    Last edited by Mathstud28; November 15th 2008 at 08:55 AM. Reason: Add in
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  4. #4
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    Interval 1 to 5, I need to find the left and right a estimated sides..
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