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Math Help - Integration - Recursive Formulae

  1. #1
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    Integration - Recursive Formulae



    I did Integration by Parts and ended up with:

    I_n = e - nI_{n-1}

    Not sure where to head from here?

    Thanks.
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  2. #2
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    Re: Integration - Recursive Formulae

    Hey eskimogenius.

    Integrating by parts gives

    I_{n-1}
    = [x^(n-1)*e^x]{0,1} - 1/n*Int{0,1}(x^n*e^(x)dx)
    = e - 1/n*I{n}

    Assuming d/dx (x^n/n) = x^(n-1).
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  3. #3
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    Re: Integration - Recursive Formulae

    Sorry, I think the question might have been wrong.

    If you sub:
    n = n+1 into the result I gave, you arrive at the answer except a + instead of - sign.
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  4. #4
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    Re: Integration - Recursive Formulae

    Quote Originally Posted by eskimogenius View Post
    Sorry, I think the question might have been wrong.
    If you sub: n = n+1 into the result I gave, you arrive at the answer except a + instead of - sign.
    You are correct as posted there is a small typo in it.
    It should be {I_{n + 1}} = e - (n + 1){I_n}.

    If you start with {I_n} = \int_0^1 {{x^n}{e^x}dx} and then use the parts decomposition u=e^x~\&~dv=x^n.

    That will give the corrected formula.
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  5. #5
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    Re: Integration - Recursive Formulae

    Integration - Recursive Formulae-31-3-13.png
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