Simpson's rule is a method for approximating integrals using a sum of quadratic functions. When using Simpson's rule, you must always use an even number of points.

Simpsons rule is written as follows:

Where and .

Example

Approximate using Simpson's rule, with .

, , .

So ,

Since

• .

Error

The error induced by Simpson's rule can be bounded by the following equation

Where is a value such that for in , is a Simpsons rule approximation using points.

Example

Considering what value of do we need to ensure that our Simpson's rule approximation is within th of the true value.

Hence must be at least .