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Math Help - Finding the antiderivative of ∫t^3*e^6t dt

  1. #1
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    Finding the antiderivative of ∫t^3*e^6t dt

    Consider finding the antiderivative of ∫t^3*e^6t dt.
    a)Find β
    b)Find the matrix [T]β for the differentiation operator T
    c)Find [T]β^-1 and use it to find ∫t^3*e^6t dt. β
    d)Use [T]β^-1 to find ∫(t^3-t^2+t-1)*e^6t dt

    The problem is that i don't really understand how to get started with finding the basis of the antiderivative
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    Re: Finding the antiderivative of ∫t^3*e^6t dt

    Quote Originally Posted by choph View Post
    Consider finding the antiderivative of ∫t^3*e^6t dt.
    a)Find β
    ??? There is no " \beta" in your formula.

    b)Find the matrix [T]β for the differentiation operator T
    c)Find [T]β^-1 and use it to find ∫t^3*e^6t dt. β
    d)Use [T]β^-1 to find ∫(t^3-t^2+t-1)*e^6t dt

    The problem is that i don't really understand how to get started with finding the basis of the antiderivative
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