Have a question which i cant seem to find a real answer for. I have been given an ellipse defined by the formula:
|x/a| ^n + |y/b| ^n = 1 (cartesian coords, a = b = 1)
x(t)=+/cos 2^n (t), y(t)=+/sin2^n(t) (paramatric coords).
I want to find the circumference, given a few diffrent n values, for example, 3. I have come accross elliptic integrals of the second kind, which will work for a and b not being equal to 1...because if it is, i just end up with the integral of 1 from 0 to Pi/2, and thinking about it, the elliptic integral of the second kind is for equations of the parametric form x(t)=cos(x) and y(t)=sin(x). How can i derive a formula for the circumference of the superellipse?