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Antiderivative to the formula f(x)=(2xr-x²)^(1/2)

  1. May 23, 2008 #1
    Hi, i cant seem to get the antiderivative to the formula f(x)=(2xr-x²)^(1/2) right. Can anyone help me out?

    By the by, if could anyone link a site with formulas for antiderivatives that would be nice.
  2. jcsd
  3. May 23, 2008 #2
    The anti-derivative you are seeking is:

    \frac{2 r^2 \sqrt{2 r-x} \sqrt{x} \tan ^{-1}\left(\frac{\sqrt{x}}{\sqrt{2 r-x}}\right)-x \left(2 r^2-3 x r+x^2\right)}{2 \sqrt{(2
    r-x) x}}

    I highly recommend this site:


    And I highly recommend the software package Mathematica that is made by this company.
  4. May 23, 2008 #3


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    Ouch. That integral hurts a lot. I wonder how to even begin doing it.
  5. May 23, 2008 #4


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    well off hand it just looks like sqrt(a^2 - u^2), after completing the square, which would make it an arcsin.
  6. May 24, 2008 #5
    Damn! I was going to intergral from 0 to 2r... Trial and error
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