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Math Help - Integration help for someone who is a little rusty

  1. #1
    Newbie
    Joined
    Feb 2009
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    7

    Integration help for someone who is a little rusty

    Hi everyone, first post and already whining for help, but ok..

    Could someone help me out a little with the following problem:

    F(x)= [(1+x)^0.5 -1]/(2^0.5 - 1) ; This represents a cumulative distribution function. I have to calculate the average by integrating "x*F'(x)" from 1 to 0.
    I'm supposed to use Integration by parts etc.

    My little help needed is: what is the integral of F(x) ==> I came up with something but I think it is wrong...[([(1+x)^1.5]/1.5)-1]/(2^0.5 - 1). Any help would be greatly appreciated!
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  2. #2
    MHF Contributor
    Joined
    Nov 2008
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    France
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    1,458
    Hi

    F(x) = \frac{\sqrt{1+x}-1}{\sqrt{2}-1}

    One antiderivative for F is

    \frac{\frac{2}{3}(1+x)^{\frac{3}{2}}-x}{\sqrt{2}-1}
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