Difference between revisions of "Length of a curve using numerical methods"
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Simpson's Rule is used to calculate integrals numerically. | Simpson's Rule is used to calculate integrals numerically. | ||
| − | From the [[Length of a curve|Length of curve page]], the length can be calculated using the integral: <font size = "+2"><span>∫</span></font>sqr(1+f '(x)<sup>2</sup>)dx | + | From the [[Length of a curve|Length of curve page]], the length can be calculated using the integral: <font size = "+2"><span>∫</span></font>sqr(1+f '(x)<sup>2</sup>)dx |
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Instead of evaluating this integral with a table, a numerical method called Simpson's rule can be used: | Instead of evaluating this integral with a table, a numerical method called Simpson's rule can be used: | ||
Revision as of 18:41, 1 April 2021
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
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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.
