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In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus, [a] the other being differentiation. Integration was initially used to solve problems in mathematics and ...
e. In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral . The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for "numerical integration", especially as applied to one-dimensional integrals.
Constant of integration. In calculus, the constant of integration, often denoted by (or ), is a constant term added to an antiderivative of a function to indicate that the indefinite integral of (i.e., the set of all antiderivatives of ), on a connected domain, is only defined up to an additive constant. [1] [2] [3] This constant expresses an ...
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 ...
Gaussian integral. A graph of the function and the area between it and the -axis, (i.e. the entire real line) which is equal to . The Gaussian integral, also known as the Euler–Poisson integral, is the integral of the Gaussian function over the entire real line. Named after the German mathematician Carl Friedrich Gauss, the integral is.
Elliptic Integrals are said to be 'complete' when the amplitude φ = π 2 and therefore x = 1. The complete elliptic integral of the first kind K may thus be defined as. or more compactly in terms of the incomplete integral of the first kind as. It can be expressed as a power series.
In mathematics (specifically multivariable calculus ), a multiple integral is a definite integral of a function of several real variables, for instance, f(x, y) or f(x, y, z). Physical (natural philosophy) interpretation: S any surface, V any volume, etc.. Incl. variable to time, position, etc.
Integral equation. For equations of integer unknowns, see Diophantine equation. In mathematics, integral equations are equations in which an unknown function appears under an integral sign. [1] In mathematical notation, integral equations may thus be expressed as being of the form: where is an integral operator acting on u. [1]
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