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

[greghouse]

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.

 

[Crosson]

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:

http://integrals.wolfram.com/index.jsp

And I highly recommend the software package Mathematica that is made by this company.

 

[Defennder]

Ouch. That integral hurts a lot. I wonder how to even begin doing it.

 

[mathwonk]

well off hand it just looks like sqrt(a^2 - u^2), after completing the square, which would make it an arcsin.

 

[greghouse]

Damn! I was going to intergral from 0 to 2r... Trial and error