In computer science, in the field of numerical analysis, Simpson's Rule is a way to get an approximation of an integral:
Proof
We want to have our polynomial on the form:
As this Simpson's rule apply to equidistant points, we know that and that . This means we may transport our solution to the intervals formed by such that
We need to interpolate these values and function values with a polynomial and form our equations:
To examine the accuracy of the rule, take , so
Error of Simpson's Rule
Using integration by parts we get:
we have