In mathematics, the integral of a function of several variables defined on a line or curve that has been expressed in terms of arc length (see length of a curve). An ordinary definite integral is defined over a line segment, whereas a line integral may use a more general path, such as a parabola or a circle. Line integrals are used extensively in the theory of functions of a complex variable.
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In mathematics, a function that results when a given function is multiplied by a so-called kernel function, and the product is integrated (see integration) between suitable limits. Its value lies in its ability to simplify intractable differential equations (subject to particular boundary conditions) by transforming the derivatives and boundary conditions into terms of an algebraic equation that may easily be solved. The solution yielded must be converted to the final solution using an inverse transformation. Several integral transforms are named for the mathematicians who introduced them (Fourier transform, Laplace transform).
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In mathematics, an equation with an unknown function within an integral. An example is
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In calculus, the process of finding a function whose derivative is a given function. The term, sometimes used interchangeably with “antidifferentiation,” is indicated symbolically with the integral sign ∫. (The differential math.dmath.x usually follows to indicate math.x as the variable.) The basic rules of integration are: (1) ∫(math.f + math.g)math.dmath.x = ∫math.fmath.dmath.x + ∫math.gmath.dmath.x (where math.f and math.g are functions of the variable math.x), (2) ∫math.kmath.fmath.dmath.x = math.k∫math.fmath.dmath.x (math.k is a constant), and (3)
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International association of Latin American countries originally dedicated to improving its members' economic well-being through free trade. At its founding in 1960 LAFTA included Argentina, Brazil, Chile, Mexico, Paraguay, Peru, and Uruguay; by 1970 Ecuador, Colombia, Venezuela, and Bolivia had joined. The organization aimed to remove all trade barriers over 12 years, but its members' geographic and economic diversity made that goal impossible. LAFTA was superseded in 1980 by the LAIA, which established bilateral trading agreements between members, which were divided into three groups according to their level of economic development. Cuba was admitted with observer status in 1986, and it became a full member in 1999. Seealso Inter-American Development Bank.
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Fundamental concept of calculus related to areas and other quantities modeled by functions. A definite integral gives the area between the graph of a function and the horizontal axis between vertical lines at the endpoints of an interval. It also calculates the net change in a system over an interval, thus leading to formulas for the work done by a varying force or the distance traveled by an object moving at varying speeds. When only the function is given, with no interval, it is known as an indefinite integral. The process of solving either a definite or an indefinite integral is called integration. According to the fundamental theorem of calculus, a definite integral can be calculated by using its antiderivative (a function whose rate of change, or derivative, equals the function being integrated). Integrals extend to higher dimensions through multiple integrals. Seealso line integral; surface integral.
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