# Approximating Arc Length

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Hello All, What to know is it possible to find the arc length of the parametric functions: x(t) = t, y(t) = cos(t)?. I know that this has the following integral: sqrt(1 + sin^2(t)), between the interval [t0, t1]. I'm pretty sure that this does integrate but it would take way too long for my purposes. Are there any approximate methods out there that you could recommend?. Thanks for your help, mameman.

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You've already reduced it to a simple integral so any integration approximation will work, and there is a wealth of information online for how to do this.

http://en.wikipedia.org/wiki/Numerical_integration

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It doesn't integrate in a closed form, actually. It can be expressed in terms of an elliptic integral (of the second kind), but that would seem useless for your purposes. Chalk up another vote for numerical integration. There are plenty of existing implementations out there for you to use.

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