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Thread: Limit of defined integral

  1. #1
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    Limit of defined integral

    $\displaystyle \lim_{n\rightarrow \infty}n\int_{-1}^{0}(x+e^x)^ndx$

    The answer it's suppose to be
    $\displaystyle
    \frac{1}{2}
    $
    So the value of the integral should be
    $\displaystyle
    \frac{1}{2n}
    $
    Direct integration is nonsense.
    With First mean value theorem for integration I don't obtain anything.
    Last edited by m3th0dman; Apr 16th 2009 at 05:09 AM.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    The integral does not need to be 1/ 2n

    There are an infinity of possibilites such as 1/2n -e^(-n) for example
    though this is not the answer
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