- #1
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Are there any formulas for finding the length of the line traced out by some function f()?
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...
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...