SIMPSON'S RULE

When computing Riemann sums, we approximated the height of the graph by a constant function. Using the trapezoidal rule we used a linear approximation to the graph. With Simpson’s rule we match quadratics (i.e. parabolas), instead of straight or slanted lines, to the graph. When Δx is small this approximates the curve very closely, and we get a fantastic numerical approximation of the definite integral.