Length of a curve using numerical methods
Jump to navigation
Jump to search
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:
Sn = (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.
