Simpson's Rule
An Interactive Applet powered by Sage and MathJax.
(By Kelsey Norman with HTML code from Prof. Gregory V. Bard)
\textrm{Given a function } f, \textrm{ the integral from } a \textrm{ to } b \textrm{ can be approximated by}
\\
\textrm{parabolas over } n/2 \textrm{ intervals of width } 2\Delta x, \textrm{ assuming } n \textrm{ is even. Then }
\\
\int_a^b f(x) \, dx \approx \frac{\Delta x}{3} (y_0 + 4y_1 + 2y_2 + 4y_3 + ... + 4y_{n-1} + y_n)
\\
\textrm{where each } y_i = f(x_i) \textrm{ for points } x_i = a + i\Delta x \textrm{ from an evenly-spaced}
\\
\textrm{partition of the interval } [a,b].
Last modified on July 25th, 2017.