Are there any formulas for finding the length of the line traced out by some function f()?(adsbygoogle = window.adsbygoogle || []).push({});

IE: If f(x) = cx + b where c and b are constants

The length from 0 to x is:

l(x) = sqr(x^2 + (cx)^2)

But I don't know what to do for any polynomial above a line.

I can make a summation for it, but don't know how to simplify.

l(x) = lim[t->infinity](sum[n = 0 to t](sqr( 1/x^2 + (f(x*n/t)-f(x*(n+1)/t)))^2)))

Basically the sum of arbitrarily small linear approximations.

I figure the length of sin() and cos() are related to pi somehow...

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# Length of f()

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