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.