6. Simpson's Rule
by M. Bourne
The Trapezoidal Rule is an improvement over using rectangles because we have much less "missing" from our calculations. We used straight lines to model the curve in trapezoidal Rule.
We seek an even better approximation. In Simpson's Rule, we use parabolas to approximate each part of the curve. This proves to be very efficient. (See more about Parabolas.)
We can show (by integrating the area under each parabola and adding these areas) that the approximate area is given the following. This is called Simpson's Rule:

Note: In Simpson's Rule, n must be EVEN.
In the LiveMath document, note how the approximation is very good, even with a small number of divisions.
Exercise:
Approximate
using Simpson's Rule with
n = 4.
Didn't find what you are looking for on this page? Try search:
Find your integral using Wolfram|Alpha!
This next search box allows you to enter your math problem and Mathematica solves it for you. (It's free!)
See how to enter math.
Online Algebra Solver
This algebra solver can solve a wide range of math problems. (Please be patient while it loads.)
Calculus Lessons on DVD
Easy to understand calculus lessons on DVD. See samples before you commit.
More info: Calculus videos
Ready for a break?
Play a math game.
(Well, not really a math game, but each game was made using math...)
The IntMath Newsletter
Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!
Share IntMath!
Short URL for this Page
Save typing! You can use this URL to reach this page:
intmath.com/simpsons



