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An fairly good numerical integration technique. The method is also available in the Wolfram Language using the option Method -> DoubleExponential to NIntegrate.

In order to integrate a function over a complicated domain D, Monte Carlo integration picks random points over some simple domain D^' which is a superset of D, checks whether ...

Inverse function integration is an indefinite integration technique. While simple, it is an interesting application of integration by parts. If f and f^(-1) are inverses of ...

A formula for numerical integration, (1) where C_(2n) = sum_(i=0)^(n)f_(2i)cos(tx_(2i))-1/2[f_(2n)cos(tx_(2n))+f_0cos(tx_0)] (2) C_(2n-1) = ...

Integration under the integral sign is the use of the identity int_a^bdxint_(alpha_0)^alphaf(x,alpha)dalpha=int_(alpha_0)^alphadalphaint_a^bf(x,alpha)dx (1) to compute an ...

Quasi-Monte Carlo integration is a method of numerical integration that operates in the same way as Monte Carlo integration, but instead uses sequences of quasirandom numbers ...

The Euler-Maclaurin integration and sums formulas can be derived from Darboux's formula by substituting the Bernoulli polynomial B_n(t) in for the function phi(t). ...

The term "integral" can refer to a number of different concepts in mathematics. The most common meaning is the the fundamenetal object of calculus corresponding to summing ...

The Newton-Cotes formulas are an extremely useful and straightforward family of numerical integration techniques. To integrate a function f(x) over some interval [a,b], ...

A definite integral is an integral int_a^bf(x)dx (1) with upper and lower limits. If x is restricted to lie on the real line, the definite integral is known as a Riemann ...