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  2. Order of integration (calculus) - Wikipedia

    en.wikipedia.org/wiki/Order_of_integration...

    The integral can be reduced to a single integration by reversing the order of integration as shown in the right panel of the figure. To accomplish this interchange of variables, the strip of width dy is first integrated from the line x = y to the limit x = z , and then the result is integrated from y = a to y = z , resulting in:

  3. Integration by parts - Wikipedia

    en.wikipedia.org/wiki/Integration_by_parts

    Integration by parts is a heuristic rather than a purely mechanical process for solving integrals; given a single function to integrate, the typical strategy is to carefully separate this single function into a product of two functions u(x)v(x) such that the residual integral from the integration by parts formula is easier to evaluate than the ...

  4. Preorder - Wikipedia

    en.wikipedia.org/wiki/Preorder

    Both of these are special cases of a preorder: an antisymmetric preorder is a partial order, and a symmetric preorder is an equivalence relation. Moreover, a preorder on a set can equivalently be defined as an equivalence relation on , together with a

  5. Leibniz integral rule - Wikipedia

    en.wikipedia.org/wiki/Leibniz_integral_rule

    In calculus, the Leibniz integral rule for differentiation under the integral sign, named after Gottfried Wilhelm Leibniz, states that for an integral of the form () (,), where < (), < and the integrands are functions dependent on , the derivative of this integral is expressible as (() (,)) = (, ()) (, ()) + () (,) where the partial derivative indicates that inside the integral, only the ...

  6. Integration by reduction formulae - Wikipedia

    en.wikipedia.org/wiki/Integration_by_reduction...

    To compute the integral, we set n to its value and use the reduction formula to express it in terms of the (n – 1) or (n – 2) integral. The lower index integral can be used to calculate the higher index ones; the process is continued repeatedly until we reach a point where the function to be integrated can be computed, usually when its index is 0 or 1.

  7. Order of integration - Wikipedia

    en.wikipedia.org/wiki/Order_of_integration

    In statistics, the order of integration, denoted I(d), of a time series is a summary statistic, which reports the minimum number of differences required to obtain a covariance-stationary series. Integration of order d

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    Get answers to your AOL Mail, login, Desktop Gold, AOL app, password and subscription questions. Find the support options to contact customer care by email, chat, or phone number.

  9. Numerical integration - Wikipedia

    en.wikipedia.org/wiki/Numerical_integration

    The term "numerical integration" first appears in 1915 in the publication A Course in Interpolation and Numeric Integration for the Mathematical Laboratory by David Gibb. [2] "Quadrature" is a historical mathematical term that means calculating area. Quadrature problems have served as one of the main sources of mathematical analysis.