- (ii) The errors in (NI.6,7) are written in the form:
where is some value of

**x**in . - Note that, as expected, trapezoidal formula is exact for linear
functions (error vanishes for ).
- But Simpson's rule---which as derived is exact for
quadratic ---is unexpectedly exact for cubics.
- In other words, its error is particularly small and it is a
widely used formula in its extended form:
where and are equidistant.

- One gets this formula by applying Simpson to intervals to , to to in succession.

Geoffrey Fox, Northeast Parallel Architectures Center at Syracuse University, gcf@npac.syr.edu