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Thread: Solving a definite integral

  1. #1
    Aug 2010

    Solving a definite integral


    While trying to solve an integral of the form integral of f(x)/g(x) where f(x) = Σ K(x-x_i) and g(X) = Σ K(x-x_i) where the range of i in case of f(x) is 1 to p and in the case of g(x) it is 1 to q[IMG]file:///tmp/moz-screenshot-1.png[/IMG].[IMG]file:///tmp/moz-screenshot.png[/IMG]K(x) = (1-u*u), I'm unable to understand how will I integrate a fraction which has got summation in both the numerator and the denominator.

    Help is highly appreciated. Thanks.

    Moderator edit: The followng has been concatenated from another (now deleted) duplicate thread started by the OP:

    Please find attached the pdf file in which you will find the integral which I'm trying to solve.
    I originally created a thread with a similar title but was unable to attach the file in the reply.
    Attached Thumbnails Attached Thumbnails Solving a definite integral-problem.pdf  
    Last edited by mr fantastic; Aug 20th 2010 at 04:42 AM.
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  2. #2
    Senior Member
    Jul 2010
    Your post is quite illegible:

    1. Are the sums the same, except for the range.
    2. What exactly is meant by K, (x-x_i). Is K a function of x - x_i or is it a constant?
    3. THe images don't work.

    Answering the last bit, to integrate a fraction of two sums you need to simplify those sums a bit. Do they each have an easy closed form that you know of? Can you do a partial fraction decomposition? The last one is somewhat difficult in general. If the top sum is the same as the bottom but they have different indices of summation, then maybe you can cancel some of the terms by doing long division (i.e. when the degree of the polynomial in the numerator is higher than the degree in the denominator).
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