Use a power series to approximate the definite integral to 6 decimal places:
$\displaystyle \int^{.5}_{0} ln (1+x^5) dx$
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?
Use a power series to approximate the definite integral to 6 decimal places:
$\displaystyle \int^{.5}_{0} ln (1+x^5) dx$
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?
Try this...
$\displaystyle \ln (1 + y) = \sum_{n=0}^{\infty} \frac{(-1)^n y^n}{n}$ so long as |y| < 1.
So let y = x^5 to get $\displaystyle \ln (1 + x^5) = \sum_{n=0}^{\infty} \frac{(-1)^n x^{5n}}{n}$ and integrate the first few terms then sub in x=0.5.