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Math Help - Riemann's sum question

  1. #1
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    Riemann's sum question

    Express the integral as a limit of Riemann sums. Do not evaluate the limit.


    Answer I got for this is...

    (2+5/ni) - 3ln(2+5/ni) * 5/n.

    I thought it was right, but apparently it's wrong.
    Last edited by Jgirl689; May 10th 2010 at 01:14 PM.
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  2. #2
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    Quote Originally Posted by Jgirl689 View Post
    Express the integral as a limit of Riemann sums. Do not evaluate the limit.


    Answer I got for this is...

    (2+5/ni) - 3ln(2+5/ni) * 5/n.

    I thought it was right, but apparently it's wrong.

    As the function in the integral is continuous is [2,7] we know the integral exists and thus we can choose the partition of the interval as we want. We choose

    to subdivide [2,7] in n subintervals of equal length \frac{7-2}{n}=\frac{5}{n} , and we evaluate the function at right end of each subinterval:

    \lim_{n\to\infty}\sum^n_{i=i}\frac{5}{n}\left[2+\frac{5i}{n}-3\ln\left(2+\frac{5i}{n}\right)\right] ...this looks similar to what you got but I can't be sure since it isn't clear the way you wrote it.

    Tonio
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