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Approximate an integral using Taylor/Maclaurin series

  1. Feb 25, 2012 #1
    Please give only hints, no full solutions :)

    1. The problem statement, all variables and given/known data

    Use series to approximate the definite integral to within the indicated accuracy:
    [itex]\int_0^{0.1} \frac{dx}{\sqrt{1 + x^3}}[/itex], [itex]|\text{error}| < 10^{-8}[/itex]

    2. Relevant equations

    Taylor series and Maclaurin series

    3. The attempt at a solution

    This doesn't seem to match or bear resemblance to any of the "famous" ones which can easily be expressed with series [itex]e^x, \sin{x}, \cos{x}[/itex], and I tried taking seven derivatives, but this is awfully annoying. Are there any other methods?

    Last edited: Feb 25, 2012
  2. jcsd
  3. Feb 25, 2012 #2


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    Try expanding ##(1+x^3)^{-1/2}## as a binomial series.
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