Home | 18.01 | Chapter 16 | Section 16.1

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Why use Simpson's rule?

Why these weigths? Because they are exactly correct even for n = 2 if f is a cubic polynomial.

Suppose: f(x) = a0 + a1x + a2x2 + a3x3

Calculate using Simpson's rule with n = 2.


Thus Simpson's rule, with n = 2 is the exact integral on any cubic! 

As a consequence of this fact, if we ide our interval into pieces in each of which f is not far from a cubic, Simpson's rule will be very accurate.