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Math Help - Riemann Sums

  1. #1
    Newbie
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    May 2008
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    Riemann Sums

    Hi,

    we've been asked to find the L(f,Pn) of the function f(x)= sin(x) over the interval [0,a] where 0 ˂ a ≤ 1 and the partition of the interval into n subintervals of even length and find the lim [L(f,Pn)]
    n

    we are also given:

    n
    ∑ sin(ix) = [[sin(x(n+1)/2)sin(nx/2)]/sin(x/2)]
    i=1

    Would really appreciate the help.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Number Cruncher 20 View Post
    Hi,

    we've been asked to find the L(f,Pn) of the function f(x)= sin(x) over the interval [0,a] where 0 ˂ a ≤ 1 and the partition of the interval into n subintervals of even length and find the lim [L(f,Pn)]
    n

    we are also given:

    n
    ∑ sin(ix) = [[sin(x(n+1)/2)sin(nx/2)]/sin(x/2)]
    i=1

    Would really appreciate the help.
    .

    If I understand your notation correctly, in this case:

    L(f,Pn)=(a/n) \sum_{i=0}^{n-1} \sin(i(a/n))

    which may be summed using the given:

    L(f,Pn)=(a/n) \frac{\sin\left(\frac{a(n+1)}{2n}\right)\sin(\frac  {a}{2})}{\sin(\frac{a}{2n})}

    Now hopefully evaluating this limit will give the required answer.

    RonL
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