




If f is expanded in a power series within each interval of size 2Dx about the interval's center, the error in each cubic approximation is of the order of c(Dx)^{4} which goes as n^{  4}.
There are such intervals, so that even if these errors accumulate (as they often don't) the resulting error will behave like n ^{ 3}.
The error in the trapezoid method goes to zero more like ; much more slowly than the error in Simpson's rule does.