Simpson’s Rule

With regards to a recent post on The Simpson’s triangles. We know that Simpson’s is quite a witty show. So is there a rule?

Yes! And this rule is called Simpson’s Rule! But what does it do?

Simpson’s Rule lets us estimate the area under a curve, this is akin to drawing rectangles at the curve and finding the area. The trick is that we require the values of an odd number of coordinates, including the those at both ends.

Simpson’s rule can be derived by approximating the integrand f (x) (in blue) by the quadratic interpolant P(x) (in red). From Wikipedia.

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