Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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?

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

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Try expanding ##(1+x^3)^{-1/2}## as a binomial series.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook