Comparison of integration rules in the case of very narrow chromatographic peaks

Theory of peak integration is revised for very narrow peaks. It is shown, that Trapezoidal rule area is efficient estimate of full peak area with extraordinary low error. Simpson's rule is less efficient in full area integration. Theoretical conclusions are illustrated by digital simulation and processing of experimental data. It was shown that for Gaussian peak Trapezoidal rule requires 0.62 points per standard deviation (2.5 points per peak width at baseline) to achieve integration error of only 0.1%, while Simpson's rule requires 1.8 times higher data rates. Asymmetric peaks require higher data rates as well. Reasons of poor behavior of Simpson's rule are discussed; averaged Simpson's rules are constructed, these rules coincide with those based on Euler-Maclaurin formula. Euler-Maclaurin rules can reduce error in the case of partial peak integration. Higher peak moments (average retention time, dispersion, skewness, etc.) also exhibit extraordinary low errors and can potentially be used for evaluation of peak shape.