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). Integrals of a function...

calculus, a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analogue of the...

In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process...

calculus), a volume integral (∭) is an integral over a 3-dimensional domain; that is, it is a special case of multiple integrals. Volume integrals are especially...

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...

mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. The terms path integral, curve integral, and curvilinear...

as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval. It...

several integrals known as the Dirichlet integral, after the German mathematician Peter Gustav Lejeune Dirichlet, one of which is the improper integral of...

Integration is the basic operation in integral calculus. While differentiation has straightforward rules by which the derivative of a complicated function...

In mathematics, an integral transform is a type of transform that maps a function from its original function space into another function space via integration...

one-dimensional integrals. To compute integrals in multiple dimensions, one approach is to phrase the multiple integral as repeated one-dimensional integrals by applying...

antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a continuous function f is a differentiable function F whose...

infinitesimals", it has two major branches, differential calculus and integral calculus. The former concerns instantaneous rates of change, and the slopes...

It is key for the notion of iterated integrals that this is different, in principle, from the multiple integral ∬ f ( x , y ) d x d y . {\displaystyle...

determinant also appears when changing the variables in multiple integrals (see substitution rule for multiple variables). When m = 1, that is when f : Rn → R...

the Leibniz integral rule for differentiation under the integral sign, named after Gottfried Wilhelm Leibniz, states that for an integral of the form...

The Gaussian integral, also known as the Euler–Poisson integral, is the integral of the Gaussian function f ( x ) = e − x 2 {\displaystyle f(x)=e^{-x^{2}}}...

improper integral is an extension of the notion of a definite integral to cases that violate the usual assumptions for that kind of integral. In the context...

of multiple types of integration, including line integrals, surface integrals and volume integrals. Due to the non-uniqueness of these integrals, an...

the integral sign Trigonometric substitution Partial fractions in integration Quadratic integral Proof that 22/7 exceeds π Trapezium rule Integral of the...

Integral theory as developed by Ken Wilber is a synthetic metatheory aiming to unify a broad spectrum of Western theories and models and Eastern meditative...

complex analysis, contour integration is a method of evaluating certain integrals along paths in the complex plane. Contour integration is closely related...

transforms iterated integrals (or multiple integrals through the use of Fubini's theorem) of functions into other, hopefully simpler, integrals by changing the...

reverse chain rule or change of variables, is a method for evaluating integrals and antiderivatives. It is the counterpart to the chain rule for differentiation...

The path integral formulation is a description in quantum mechanics that generalizes the stationary action principle of classical mechanics. It replaces...

and for single and double integrals. The integration formula for double integrals may be generalized to any multiple integral. In all cases, there is a...

perpendicular to the plane). In both cases, it is calculated with a multiple integral over the object in question. Its dimension is L (length) to the fourth...

fractional derivative and integral has multiple applications such as in case of solutions to the equation in the case of multiple systems such as the tokamak...

The INTErnational Gamma-Ray Astrophysics Laboratory (INTEGRAL) is a space telescope for observing gamma rays of energies up to 8 MeV. It was launched by...

analysis and analytic geometry preliminary to the study of differential and integral calculus." He began with the fundamental concepts of variables and functions...