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Line 5: − There are two types of integrals. Definite integrals are integrals that are evaluated over limits of integration. Indefinite integrals are not evaluated over limits of integration. Evaluating an indefinite integral yields the antiderivative of the integrand plus a constant of integration. − Integration has many physical applications. The indefinite integral of an [[acceleration]] function with respect to time gives the [[velocity]] function defined to within a constant, while the definite integral of an acceleration function with respect to time gives the change in velocity between the upper and lower limits of integration. Likewise, the indefinite integral of a time function of velocity with respect to time gives the position function defined to within a constant, and the definite integral of this velocity function will give the change in position between the two limits of integration. + + + + + + + + Line 58:
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reorganized information and added links in See also section
where ''a'' and ''b'' represent the lower and upper bounds of the [[interval]] being integrated over, ''f(x)'' represents the function being integrated (the '''integrand'''), and ''dx'' represents a dummy variable given various definitions, depending on the context of the integral.
where ''a'' and ''b'' represent the lower and upper bounds of the [[interval]] being integrated over, ''f(x)'' represents the function being integrated (the '''integrand'''), and ''dx'' represents a dummy variable given various definitions, depending on the context of the integral.
==Integration==
Integration is the inverse function of the [[derivative]] and the two notions are related by the [[Fundamental Theorem of Calculus]].
Integration is the inverse function of the [[derivative]] and the two notions are related by the [[Fundamental Theorem of Calculus]].
The concept of integration can be extended to functions in more than one real variable, as well as functions defined over the [[complex numbers]].
The concept of integration can be extended to functions in more than one real variable, as well as functions defined over the [[complex numbers]].
Integration has many physical applications. The indefinite integral of an [[acceleration]] function with respect to time gives the [[velocity]] function defined to within a constant, while the definite integral of an acceleration function with respect to time gives the change in velocity between the upper and lower limits of integration. Likewise, the indefinite integral of a time function of velocity with respect to time gives the position function defined to within a constant, and the definite integral of this velocity function will give the change in position between the two limits of integration.
==Types of Integrals==
There are two types of integrals. [[Definite integral|Definite integrals]] are integrals that are evaluated over limits of integration. [[Indefinite integral|Indefinite integrals]] are not evaluated over limits of integration. Evaluating an indefinite integral yields the antiderivative of the integrand plus a constant of integration.
==Properties of integrals==
==Properties of integrals==
*[[Methods of integration]]
*[[Methods of integration]]
*[[Definite integral]]
*[[Definite integral]]
*[[Indefinite integral]]
===External Links===
===External Links===
[http://mathworld.wolfram.com/Integral.html Integrals - Wolfram MathWorld]
[http://mathworld.wolfram.com/Integral.html Integrals - Wolfram MathWorld]