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Homework Help: Arc Length of Ellipse, Hard Integral

  1. Apr 16, 2012 #1
    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. jcsd
  3. Apr 16, 2012 #2


    User Avatar
    Gold Member

    Check out the term elliptic integrals. You will find a fully developed theory behind this whole area.
  4. Apr 16, 2012 #3
    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."
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