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

  • Thread starter greghouse
  • Start date
  • #1
37
0

Main Question or Discussion Point

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.
 

Answers and Replies

  • #2
1,250
2
The anti-derivative you are seeking is:

[tex]
\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}}
[/tex]

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.
 
  • #3
Defennder
Homework Helper
2,591
5
Ouch. That integral hurts a lot. I wonder how to even begin doing it.
 
  • #4
mathwonk
Science Advisor
Homework Helper
10,764
937
well off hand it just looks like sqrt(a^2 - u^2), after completing the square, which would make it an arcsin.
 
  • #5
37
0
Damn! I was going to intergral from 0 to 2r... Trial and error
 

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

  • Last Post
Replies
9
Views
54K
  • Last Post
Replies
4
Views
3K
  • Last Post
2
Replies
28
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
2K
Replies
3
Views
6K
Replies
2
Views
2K
Top