# What is an easy way to calculate numerical integration uncertainty/error

1. Jun 16, 2011

### jephthah

i'm measuring a waveform (pulse) that i want to integrate the area under.

i take a bunch of samples and use one of the basic numeric integration methods (Trapezoidal, Simpson's, Boole's)

what is a fairly easy method to estimate the uncertainty/error of the numeric integration compared to the "true" value?

thanks

2. Jun 16, 2011

### gb7nash

For Simpson's Rule, the error bound is:

$$\frac{1}{90}(\frac{b-a}{2})^5 |f''''(z)|$$ where z is the number between a and b that maximizes |f''''(x)| between a and b.

I got this from:

http://en.wikipedia.org/wiki/Simpson's_rule

You can find the other's on wiki as well. As far as an easier method of determining the error, I'm not aware of any. Since these methods are in some way, shape or form derived from Taylor approximations, I'm pretty sure you can't rid of taking a number of derivatives.