# Arc Length of Ellipse, Hard Integral

1. Apr 16, 2012

### Swimmingly!

1. The problem statement, all variables and given/known data
Find the arc length of the ellipse or deformed circle. r^2=x^2+(y/β)^2

β=dilation constant
k="random" constant

2. Relevant equations

3. The attempt at a solution
I suspect it's impossible but I can't prove that.
After working it out I got stuck with these integrals which I can not solve:

2. Apr 16, 2012

### OldEngr63

Check out the term elliptic integrals. You will find a fully developed theory behind this whole area.

3. Apr 16, 2012

### Swimmingly!

Thanks. I had googled some pages that hinted at that but this statement in wiki about "elliptic integrals" confirmed it: "In general, elliptic integrals cannot be expressed in terms of elementary functions."