# Thread: approximating definite integral using power series

1. ## approximating definite integral using power series

Use a power series to approximate the definite integral to 6 decimal places:

$\int^{.5}_{0} ln (1+x^5) dx$

Need some help getting started on this and also how to evaluate it at the limits. Would I take the limit as n -> .5 somehow?

2. Try this...
$\ln (1 + y) = \sum_{n=0}^{\infty} \frac{(-1)^n y^n}{n}$ so long as |y| < 1.
So let y = x^5 to get $\ln (1 + x^5) = \sum_{n=0}^{\infty} \frac{(-1)^n x^{5n}}{n}$ and integrate the first few terms then sub in x=0.5.