# Approximate an integral using Taylor/Maclaurin series

1. Feb 25, 2012

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:
$\int_0^{0.1} \frac{dx}{\sqrt{1 + x^3}}$, $|\text{error}| < 10^{-8}$

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 $e^x, \sin{x}, \cos{x}$, and I tried taking seven derivatives, but this is awfully annoying. Are there any other methods?

Thanks.

Last edited: Feb 25, 2012
2. Feb 25, 2012

### LCKurtz

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