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{{Template:Math-h}}

{{Math-h}}

An '''integral''' is a mathematical construction used in [[calculus]] to represent the area of a region in a plane bounded by the graph of a [[function]] in one [[real]] variable. [[Definite integral]]s use the following notation:  

An '''integral''' is a mathematical construction used in [[calculus]] to represent the area of a region in a plane bounded by the graph of a [[function]] in one [[real]] variable. [[Definite integral]]s use the following notation:  

==Types of Integrals==

==Types of Integrals==

There are several 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.

There are several types of integrals.  [[Definite integral]]s are integrals that are evaluated over limits of integration.  [[Indefinite integral]]s are not evaluated over limits of integration.  Evaluating an indefinite integral yields the antiderivative of the integrand plus a constant of integration.

A third type - an improper integral - is an integral in which one of the limits of integration is infinity. Evaluating an improper integral requires taking the limit of the definite integral as the appropriate limit of integration approaches infinity.

A third type - an improper integral - is an integral in which one of the limits of integration is infinity. Evaluating an improper integral requires taking the limit of the definite integral as the appropriate limit of integration approaches infinity.

Unfortunately, this function has so many discontinuities that its Riemann integral is not defined.  However, if we use the Lebesgue integral instead, the function is integrable as hoped, and has the expected value <math>0</math>.

Unfortunately, this function has so many discontinuities that its Riemann integral is not defined.  However, if we use the Lebesgue integral instead, the function is integrable as hoped, and has the expected value <math>0</math>.

==See Also==

==See also==

*[[Methods of integration]]

*[[Methods of integration]]

*[[Definite integral]]

*[[Definite integral]]

*[[Indefinite 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]

*[http://www.relativitycalculator.com/mathematical_references.shtml Some Quick and Dirty Mathematical References]

*[http://www.relativitycalculator.com/mathematical_references.shtml Some Quick and Dirty Mathematical References]