# How do i find the arc length of an implicit curve given by f[x,y]=0?

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i used the implicit function theorem to find dy/dx, then applied that to the arc length formula, but i have to integrate with respect to x and there is the implicit function y[x] inside the radical.
also, if it matters, the curve is assumed to be closed.

HallsofIvy
Homework Helper
That depends strongly on what the specific function is. What is f(x,y) for this problem?

So theres no general formula/algorithm? bummer. there is no information about the curve other than it cannot be parameterized(and trivially, cannot be put into the form y[x]

HallsofIvy
Homework Helper
I am puzzled by this. Every curve can be given some parametric functions. And every curve can be written in terms of piecewise functions. Do you mean simply that you do not know what they are or that they would be very complicated?

in general they would range in complexity. im writing a program that finds the arc length of a level curve of some function f[x,y]. do you mean every implicit curve has a parametric representation?

I second HallsofIvy assertion that any curve (at least any curve that is implicitly or explicitly defined with analytic functions) can be parametrized.