Virtual Lessons: Simpson's Rule (1/3)

Also known as Simpson’s \(\textstyle\frac{1}{3}\) Rule is a numerical integration technique that improves upon the Trapezoidal Rule by utilizing the geometry of parabolic arcs. The number of partitions \(n\) must be even.

\(\displaystyle S_n=\frac{b-a}{3n}\big( f(x_0)+4f(x_1)+2f(x_2)+\cdots+4f(x_{n-1})+2f(x_n) \big)\)

\(\displaystyle \Delta x=\frac{b-a}{n}\quad \displaystyle x_k=a+k\Delta x\)