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Math Help - Limit of Riemann sums

  1. #1
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    Limit of Riemann sums

    Express the following integral as the limit of Riemann sums using the midpoint rule.
    Do not evaluate it.

    Limit of Riemann sums-codecogseqn.gif

    Please help
    Thanks in advance
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  2. #2
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    Re: Limit of Riemann sums

    Quote Originally Posted by nubshat View Post
    Express the following integral as the limit of Riemann sums using the midpoint rule
    Click image for larger version. 

Name:	CodeCogsEqn.gif 
Views:	17 
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    You are asking us to do this for you. NO WAY!
    Note that f(x)=\frac{x^2}{x^6+1} is an even function.
    So the question reduces to 2\int_0^1 {f(x)dx} .

    To partition the interval [0,1] into n regular subdivision we get \Delta_x=\frac{1}{n}.
    Then x_k=k\cdot\Delta_x,~k=0,~1,\cdots,~n.
    The midpoints are m_k=\frac{x_k-x_{k-1}}{2},~k=1.\cdots,n.
    Now the midpoint sum is \sum\limits_{k = 1}^n {f\left( {m_k } \right)\Delta _x }
    Last edited by Plato; November 16th 2012 at 04:39 PM.
    Thanks from nubshat
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  3. #3
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    Re: Limit of Riemann sums

    Thank you very much for the help
    I got Limit of Riemann sums-codecogseqn-1-.gif as an answer
    Can someone please confirm that this is right or tell me what I did wrong?
    edit: the x is suppose to be an n
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