1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Homework Helper

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


    User Avatar
    Science Advisor
    Homework Helper

    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

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