The integration rule can be specified with the setting Method->. Rule-based strategies apply a given integration rule to each subregion to obtain integral and error estimates for that region. Uniform sampling strategies try to improve the integral estimate by uniformly increasing the density of sampling throughout the whole integration region.
One-dimensional infinite-range oscillatory integrandĪdaptive sampling strategies try to improve the integral estimate by sampling more often in subregions with a larger error estimate, typically by subdividing those subregions. Multidimensional integrand, uniform samplingĪny integrand, uniform quasi-random samplingĪny integrand, adaptive quasi-random sampling The results are then represented as areas under a curve (shown in red). In this Demonstration, we perform numerical integrations for, with and. More generally, integrals of the form can be evaluated for positive integers 1.
Any integrand, adaptive sampling, rule-based The well-known Gaussian integral can be evaluated in closed form, even though there is no elementary function equal to the indefinite integral.
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