Length of a curve using numerical methods
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Simpson's Rule is used to calculate integrals numerically.
From the Length of curve page, the length can be calculated using the integral: ∫sqr(1+f '(x)2)dx
Instead of evaluating this integral with a table, a numerical method called Simpson's rule can be used:
the length of the curve after n iterations = Ln = (Δx/3)(f(x0) + 4f(x1) + 2f(x2) + 4f(x3) +2f(x4) + ...+ 2f(xn-2) + 4f(xn-1) + f(x0))
where Δx = (b-a)/n with a and b being the boundaries and n the number of iterations of the calculation.
