Approximate an integral using Taylor/Maclaurin series

  • #1
Please give only hints, no full solutions :)

Homework Statement



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]

Homework Equations



Taylor series and Maclaurin series

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.
 
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Answers and Replies

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

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