Category: Integrals

Path integral formulation
The path integral formulation is a description in quantum mechanics that generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique classical traject
Wallis' integrals
In mathematics, and more precisely in analysis, the Wallis integrals constitute a family of integrals introduced by John Wallis.
Nonelementary integral
In mathematics, a nonelementary antiderivative of a given elementary function is an antiderivative (or indefinite integral) that is, itself, not an elementary function (i.e. a function constructed fro
List of definite integrals
In mathematics, the definite integral is the area of the region in the xy-plane bounded by the graph of f, the x-axis, and the lines x = a and x = b, such that area above the x-axis adds to the total,
Iterated integral
In multivariable calculus, an iterated integral is the result of applying integrals to a function of more than one variable (for example or ) in a way that each of the integrals considers some of the
Hadamard regularization
In mathematics, Hadamard regularization (also called Hadamard finite part or Hadamard's partie finie) is a method of regularizing divergent integrals by dropping some divergent terms and keeping the f
List of integrals of inverse hyperbolic functions
The following is a list of indefinite integrals (antiderivatives) of expressions involving the inverse hyperbolic functions. For a complete list of integral formulas, see lists of integrals. * In all
Exponential integral
In mathematics, the exponential integral Ei is a special function on the complex plane. It is defined as one particular definite integral of the ratio between an exponential function and its argument.
Differential analyser
The differential analyser is a mechanical analogue computer designed to solve differential equations by integration, using wheel-and-disc mechanisms to perform the integration. It was one of the first
Borwein integral
In mathematics, a Borwein integral is an integral whose unusual properties were first presented by mathematicians David Borwein and Jonathan Borwein in 2001. Borwein integrals involve products of , wh
Gaussian integral
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 inte
Pettis integral
In mathematics, the Pettis integral or Gelfand–Pettis integral, named after Israel M. Gelfand and Billy James Pettis, extends the definition of the Lebesgue integral to vector-valued functions on a me
Cauchy principal value
In mathematics, the Cauchy principal value, named after Augustin Louis Cauchy, is a method for assigning values to certain improper integrals which would otherwise be undefined.
Frullani integral
In mathematics, Frullani integrals are a specific type of improper integral named after the Italian mathematician . The integrals are of the form where is a function defined for all non-negative real
Visual calculus
Visual calculus, invented by Mamikon Mnatsakanian (known as Mamikon), is an approach to solving a variety of integral calculus problems. Many problems that would otherwise seem quite difficult yield t
Trigonometric integral
In mathematics, trigonometric integrals are a family of integrals involving trigonometric functions.
Integration over time
No description available.
Logarithmic integral function
In mathematics, the logarithmic integral function or integral logarithm li(x) is a special function. It is relevant in problems of physics and has number theoretic significance. In particular, accordi
Lobachevsky integral formula
In mathematics, Dirichlet integrals play an important role in distribution theory. We can see the Dirichlet integral in terms of distributions. One of those is the improper integral of the sinc functi
Continuous product
No description available.
Cavalieri's quadrature formula
In calculus, Cavalieri's quadrature formula, named for 17th-century Italian mathematician Bonaventura Cavalieri, is the integral and generalizations thereof. This is the definite integral form; the in
Duhamel's integral
In theory of vibrations, Duhamel's integral is a way of calculating the response of linear systems and structures to arbitrary time-varying external perturbation.
In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integ
Santaló's formula
In differential geometry, Santaló's formula describes how to integrate a function on the unit sphere bundle of a Riemannian manifold by first integrating along every geodesic separately and then over
Product integral
A product integral is any product-based counterpart of the usual sum-based integral of calculus. The first product integral ( below) was developed by the mathematician Vito Volterra in 1887 to solve s
Volkenborn integral
In mathematics, in the field of p-adic analysis, the Volkenborn integral is a method of integration for p-adic functions.
Sophomore's dream
In mathematics, the sophomore's dream is the pair of identities (especially the first) discovered in 1697 by Johann Bernoulli. The numerical values of these constants are approximately 1.291285997...