# Problem

Given a function of one variable, f(*x*), find the integral
of the curve on the interval [*a*, *b*].

# Assumptions

None.

# Tools

We will use sampling and polynomial interpolation.

# Process

## Simpson's Rule

Given f(*x*), *a*, and *b*, let *h* = (*b* − *a*)/2 and calculate

## Simpson's 3/8th Rule

Given f(*x*), *a*, and *b*, let *h* = (*b* − *a*)/3 and calculate

## Bools's Rule

Given f(*x*), *a*, and *b*, let *h* = (*b* − *a*)/4 and calculate

Due to a typo in a common reference, Bo*ol*e's rule is mistakenly referred to as Bo*d*e's rule.

Copyright ©2005 by Douglas Wilhelm Harder. All rights reserved.