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Math Help - Evaluate integral as a power series + find radius of conv.

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    Question 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.
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    Quote Originally Posted by grib90 View Post
    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.
    \int e^{-t^3} dt = \int 1 - t^3 + \frac{t^6}{2!}-\frac{t^9}{3!}+... dt
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    Quote Originally Posted by ThePerfectHacker View Post
    \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

    \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?
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    Quote Originally Posted by grib90 View Post
    Thanks for the reply,
    Now I have

    \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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