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70 relations: Antiderivative (complex analysis), Area, Augustin-Louis Cauchy, Bounded function, Calculus, Cauchy formula for repeated integration, Cengage, Computer algebra system, Constant function, Constant of integration, Continuous function, Countable set, Darboux's theorem (analysis), Dense set, Derivative, Differential Galois theory, Disjoint union, Dominated convergence theorem, Elementary function, Error function, Exponential function, Fatou's lemma, Fσ set, Fresnel integral, Function (mathematics), Fundamental theorem of calculus, Graph of a function, Henstock–Kurzweil integral, Indefinite sum, Infinite set, Integral, Integral of inverse functions, Integration by parts, Integration by substitution, Intermediate value theorem, Interval (mathematics), Inverse trigonometric functions, Jacobian matrix and determinant, Khan Academy, Lebesgue integration, Lebesgue measure, Linearity of integration, List of trigonometric identities, Lists of integrals, Logarithm, Logarithmic integral function, Maxima (software), Meagre set, Mean value theorem, Multiple integral, ..., Natural logarithm, Nonelementary integral, Numerical integration, Partial fraction decomposition, Pathological (mathematics), Polar coordinate system, Polynomial, Rational function, Rational number, Riemann integral, Risch algorithm, Stokes' theorem, Symbolic integration, Telescoping series, Trigonometric functions, Trigonometric integral, Value (mathematics), Vertical translation, Wolfram Mathematica, 0. Expand index (20 more) »
Antiderivative (complex analysis)
In complex analysis, a branch of mathematics, the antiderivative, or primitive, of a complex-valued function g is a function whose complex derivative is g. More precisely, given an open set U in the complex plane and a function g:U\to \mathbb C, the antiderivative of g is a function f:U\to \mathbb C that satisfies \frac.
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Area
Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.
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Augustin-Louis Cauchy
Baron Augustin-Louis Cauchy FRS FRSE (21 August 178923 May 1857) was a French mathematician, engineer and physicist who made pioneering contributions to several branches of mathematics, including: mathematical analysis and continuum mechanics.
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Bounded function
In mathematics, a function f defined on some set X with real or complex values is called bounded, if the set of its values is bounded.
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Calculus
Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.
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Cauchy formula for repeated integration
The Cauchy formula for repeated integration, named after Augustin Louis Cauchy, allows one to compress n antidifferentiations of a function into a single integral (cf. Cauchy's formula).
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Cengage
Cengage is an educational content, technology, and services company for the higher education, K-12, professional, and library markets worldwide.
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Computer algebra system
A computer algebra system (CAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists.
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Constant function
In mathematics, a constant function is a function whose (output) value is the same for every input value.
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Constant of integration
In calculus, the indefinite integral of a given function (i.e., the set of all antiderivatives of the function) on a connected domain is only defined up to an additive constant, the constant of integration.
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Continuous function
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
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Countable set
In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.
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Darboux's theorem (analysis)
In mathematics, Darboux's theorem is a theorem in real analysis, named after Jean Gaston Darboux.
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Dense set
In topology and related areas of mathematics, a subset A of a topological space X is called dense (in X) if every point x in X either belongs to A or is a limit point of A, that is the closure of A is constituting the whole set X. Informally, for every point in X, the point is either in A or arbitrarily "close" to a member of A — for instance, every real number either is a rational number or has a rational number arbitrarily close to it (see Diophantine approximation).
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Derivative
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
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Differential Galois theory
In mathematics, differential Galois theory studies the Galois groups of differential equations.
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Disjoint union
In set theory, the disjoint union (or discriminated union) of a family of sets is a modified union operation that indexes the elements according to which set they originated in.
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Dominated convergence theorem
In measure theory, Lebesgue's dominated convergence theorem provides sufficient conditions under which almost everywhere convergence of a sequence of functions implies convergence in the L1 norm.
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Elementary function
In mathematics, an elementary function is a function of one variable which is the composition of a finite number of arithmetic operations, exponentials, logarithms, constants, and solutions of algebraic equations (a generalization of ''n''th roots).
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Error function
In mathematics, the error function (also called the Gauss error function) is a special function (non-elementary) of sigmoid shape that occurs in probability, statistics, and partial differential equations describing diffusion.
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Exponential function
In mathematics, an exponential function is a function of the form in which the argument occurs as an exponent.
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Fatou's lemma
In mathematics, Fatou's lemma establishes an inequality relating the Lebesgue integral of the limit inferior of a sequence of functions to the limit inferior of integrals of these functions.
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Fσ set
In mathematics, an Fσ set (said F-sigma set) is a countable union of closed sets.
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Fresnel integral
Plots of ''S''(''x'') and ''C''(''x''). The maximum of ''C''(''x'') is about 0.977451424. If \frac\pi2t^2 were used instead of t^2, then the image would be scaled vertically and horizontally (see below). Fresnel integrals, S(x) and C(x), are two transcendental functions named after Augustin-Jean Fresnel that are used in optics, which are closely related to the error function (erf).
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Fundamental theorem of calculus
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function with the concept of integrating a function.
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Graph of a function
In mathematics, the graph of a function f is, formally, the set of all ordered pairs, and, in practice, the graphical representation of this set.
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Henstock–Kurzweil integral
In mathematics, the Henstock–Kurzweil integral or gauge integral (also known as the (narrow) Denjoy integral (pronounced), Luzin integral or Perron integral, but not to be confused with the more general wide Denjoy integral) is one of a number of definitions of the integral of a function.
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Indefinite sum
In mathematics the indefinite sum operator (also known as the antidifference operator), denoted by \sum _x or \Delta^, is the linear operator, inverse of the forward difference operator \Delta.
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Infinite set
In set theory, an infinite set is a set that is not a finite set.
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Integral
In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.
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Integral of inverse functions
In mathematics, integrals of inverse functions can be computed by means of a formula that expresses the antiderivatives of the inverse f^ of a continuous and invertible function f, in terms of f^ and an antiderivative of f. This formula was published in 1905 by Charles-Ange Laisant.
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Integration by parts
In calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of their derivative and antiderivative.
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Integration by substitution
In calculus, integration by substitution, also known as u-substitution, is a method for finding integrals.
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Intermediate value theorem
In mathematical analysis, the intermediate value theorem states that if a continuous function, f, with an interval,, as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval.
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Interval (mathematics)
In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.
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Inverse trigonometric functions
In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains).
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Jacobian matrix and determinant
In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.
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Khan Academy
Khan Academy is a non-profit educational organization created in 2006 by educator Salman Khan with a goal of creating a set of online tools that help educate students.
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Lebesgue integration
In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that function and the -axis.
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Lebesgue measure
In measure theory, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of n-dimensional Euclidean space.
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Linearity of integration
In calculus, the integral of any linear combination of functions equals the same linear combination of the integrals of the functions; this property is known as linearity of integration.
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List of trigonometric identities
In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables where both sides of the equality are defined.
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Lists of integrals
Integration is the basic operation in integral calculus.
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Logarithm
In mathematics, the logarithm is the inverse function to exponentiation.
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Logarithmic integral function
In mathematics, the logarithmic integral function or integral logarithm li(x) is a special function.
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Maxima (software)
Maxima is a computer algebra system (CAS) based on a 1982 version of Macsyma.
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Meagre set
In the mathematical fields of general topology and descriptive set theory, a meagre set (also called a meager set or a set of first category) is a set that, considered as a subset of a (usually larger) topological space, is in a precise sense small or negligible.
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Mean value theorem
In mathematics, the mean value theorem states, roughly, that for a given planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints.
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Multiple integral
The multiple integral is a definite integral of a function of more than one real variable, for example, or.
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Natural logarithm
The natural logarithm of a number is its logarithm to the base of the mathematical constant ''e'', where e is an irrational and transcendental number approximately equal to.
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Nonelementary integral
In mathematics, a nonelementary antiderivative of a given elementary function is an antiderivative that is, itself, not an elementary function (i.e. a function constructed from a finite number of quotients of constant, algebraic, exponential, and logarithmic functions using field operations).
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Numerical integration
In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations.
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Partial fraction decomposition
In algebra, the partial fraction decomposition or partial fraction expansion of a rational function (that is, a fraction such that the numerator and the denominator are both polynomials) is the operation that consists in expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.
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Pathological (mathematics)
In mathematics, a pathological phenomenon is one whose properties are considered atypically bad or counterintuitive; the opposite is well-behaved.
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Polar coordinate system
In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.
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Polynomial
In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
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Rational function
In mathematics, a rational function is any function which can be defined by a rational fraction, i.e. an algebraic fraction such that both the numerator and the denominator are polynomials.
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Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.
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Riemann integral
In the branch of mathematics known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval.
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Risch algorithm
In symbolic computation (or computer algebra), at the intersection of mathematics and computer science, the Risch algorithm is an algorithm for indefinite integration.
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Stokes' theorem
In vector calculus, and more generally differential geometry, Stokes' theorem (also called the generalized Stokes theorem or the Stokes–Cartan theorem) is a statement about the integration of differential forms on manifolds, which both simplifies and generalizes several theorems from vector calculus.
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Symbolic integration
In calculus, symbolic integration is the problem of finding a formula for the antiderivative, or indefinite integral, of a given function f(x), i.e. to find a differentiable function F(x) such that This is also denoted.
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Telescoping series
In mathematics, a telescoping series is a series whose partial sums eventually only have a fixed number of terms after cancellation.
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Trigonometric functions
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.
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Trigonometric integral
In mathematics, the trigonometric integrals are a family of integrals involving trigonometric functions.
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Value (mathematics)
In mathematics, value may refer to several, strongly related notions.
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Vertical translation
In geometry, a vertical translation (also known as vertical shift) is a translation of a geometric object in a direction parallel to the vertical axis of the Cartesian coordinate system.
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Wolfram Mathematica
Wolfram Mathematica (usually termed Mathematica) is a modern technical computing system spanning most areas of technical computing — including neural networks, machine learning, image processing, geometry, data science, visualizations, and others.
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0
0 (zero) is both a number and the numerical digit used to represent that number in numerals.
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Anti-derivative, Antiderivatives, Antidifferentation, Antidifferentiation, General integral, Indefinate integrals, Indefinite integral, Indefinite integrals, Indefinite integration, Primitive (integral), Primitive function, Primitive integral, Primitive integration.
References
[1] https://en.wikipedia.org/wiki/Antiderivative
