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Limits & Riemman Sum

  1. May 5, 2008 #1
    1. The problem statement, all variables and given/known data
    Question regarding #16


    2. Relevant equations

    Riemman Sum

    3. The attempt at a solution

    I know that the limit of the Riemman Sum is basically the integral. However, I do not know where to go from there. Do I need to use the Summation formulas? Thanks
  2. jcsd
  3. May 5, 2008 #2


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    can you write down the expression for a Riemann integral. something like:

    [tex] \int_a^b f(x) dx = \lim_{N \to \infty} \sum_{n=1}^N ??? [/tex]

    what goes in the question marks?

    also, even though Riemann doesn't, assume things in the ??? are equally spaced. that's usually good enough.
    Last edited: May 5, 2008
  4. May 6, 2008 #3
    Well, here's what I have so far:

    [tex] \int_a^b f(x) dx = \lim_{N \to \infty} \sum_{n=1}^N (\frac{1}{N}\sin(\frac{\pi i}{N})[/tex]
  5. May 6, 2008 #4


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    So what part of that sum is dx and what part is f(x)? After you know f(x), what is its integral?
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