# Thread: Evaluate integral as a power series + find radius of conv.

1. ## Evaluate integral as a power series + find radius of conv.

Evaluate integral as a power series and find the radius of convergence.

f(x) = [e^(-t^3)]dt

Very few helpful examples of these in my book so any help is appreciated.

2. Originally Posted by grib90
Evaluate integral as a power series and find the radius of convergence.

f(x) = [e^(-t^3)]dt

Very few helpful examples of these in my book so any help is appreciated.
$\displaystyle \int e^{-t^3} dt = \int 1 - t^3 + \frac{t^6}{2!}-\frac{t^9}{3!}+... dt$

3. Originally Posted by ThePerfectHacker
$\displaystyle \int e^{-t^3} dt = \int 1 - t^3 + \frac{t^6}{2!}-\frac{t^9}{3!}+... dt$
Now I have

$\displaystyle \int e^{-t^3}=\int \sum_{n=0}^\infty\frac{(-1)^n*t^{3n}}{n!}*dt = C + \sum_{n=0}^\infty {(-1)^n}$

Now how do I deal with that factorial when integrating?

4. Originally Posted by grib90
$\displaystyle \int e^{-t^3}=\int \sum_{n=0}^\infty\frac{(-1)^n*t^{3n}}{n!}*dt = C + \sum_{n=0}^\infty {(-1)^n}$