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.
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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 $
Originally Posted by ThePerfectHacker $\displaystyle \int e^{-t^3} dt = \int 1 - t^3 + \frac{t^6}{2!}-\frac{t^9}{3!}+... dt $ Thanks for the reply, 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?
Originally Posted by grib90 Thanks for the reply, 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? Something went wrong in that last line. What about the factorial? It doesn't depend on t so for the integration it is simply a constant. -Dan
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