Web Reference: With the trapezoidal rule, we approximated the curve by using piecewise linear functions. What if we were, instead, to approximate a curve using piecewise quadratic functions? With Simpson’s rule, we do just this. We partition the interval into an even number of subintervals, each of equal width. Apr 20, 2022 · We discuss how as a result of this, Simpson’s rule yields a more accurate approximation of the area under the curve than any of the previous methods we have looked at and compare the... Simpson’s Rule, named after Thomas Simpson though also used by Kepler a century before, was a way to approximate integrals without having to deal with lots of narrow rectangles (which also implies lots of decimal calculations).
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