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Math Help - definite integral integration

  1. #1
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    definite integral integration

    0
    S x/sqrt(x+1) dx
    -1
    Any help would be greatly appreciated.


    I tried setting:

    u = x
    du = dx
    dv = 1/sqroot(x+1)
    v = 2sqroot(x+1)

    But everything is going to zero..
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  2. #2
    Moo
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    Quote Originally Posted by 2clients View Post
    0
    S x/sqrt(x+1) dx
    -1
    Any help would be greatly appreciated.


    I tried setting:

    u = x
    du = dx
    dv = 1/sqroot(x+1)
    v = 2sqroot(x+1)

    But everything is going to zero..
    What's wrong ?

    Using this integration by parts, you get :

    \int_{-1}^0 \frac{x}{\sqrt{x+1}} ~ dx=\left[uv\right]_{-1}^0-\int_{-1}^0 vdu

    =\left[2x \sqrt{x+1}\right]_{-1}^0-\int_{-1}^0 2 \sqrt{x+1} ~ dx

    =\left[2x \sqrt{x+1}\right]_{-1}^0-2 \int_{-1}^0 (x+1)^{1/2} ~ dx

    For the integral that's left, remember that \int x^n ~ dx=\frac{x^{n+1}}{n+1}
    If you don't see what to do, substitute u=x+1


    My final answer is something like -\frac 43
    Last edited by Moo; November 17th 2008 at 11:07 AM. Reason: tiny typo
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