Math Help - [SOLVED] Integral estimation

1. [SOLVED] Integral estimation

Using 20 terms, estimate f(0.6) where
$f(x) = \int_0^x \frac{dt}{1 + t^3}$
The student was trying to do this using a geometric series to represent the integrand. I haven't yet looked it up in my Calc book, but if I ever knew the method I've completely forgotten it. Any takers?

Thanks!
-Dan

2. $f(x) = \int_0^x {\left\{ {\sum\limits_{k\, = \,0}^\infty {( - 1)^k t^{3k} } } \right\}\,dt} .$

After interchanging sum & integral you'll get its series representation.

3. Originally Posted by Krizalid
$f(x) = \int_0^x {\left\{ {\sum\limits_{k\, = \,0}^\infty {( - 1)^k t^{3k} } } \right\}\,dt} .$

After interchanging sum & integral you'll get its series representation.