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Methods for approximating integrals

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This article is about different methods of approximating definite integrals.

Method 1: Classical approximation methods

Amongst the methods it eventually discusses (some of them perhaps in articles linked to from this one) should be the midpoint rule, the trapezium rule, Simpson's rule, approximation by the polynomial that agrees with your function at equally spaced points, Gaussian quadrature, and others.

Method 2: Approximate the integrand by a main term plus an error

If f uniformly approximates g on a bounded interval, then their integrals on that interval are close.

(more to be written)

Method 3: the principle of stationary phase

Discussed on this page.