Changes

An '''integral''' is a mathematical construction used in [[Calculus]] to represent the area of a region in a plane. Integrals use the following notation:  

An '''integral''' is a mathematical construction used in [[Calculus]] to represent the area of a region in a plane. Integrals use the following notation:  

<math>\int_a^b f(x)dx</math>

<math>\int_a^b f(x)dx</math>

where ''a'' and ''b'' represent the lower and upper bounds of the interval being integrated over, ''f'' represents the function being integrated (the '''integrand'''), and ''dx'' represents a dummy variable given various definitions, depending on the context of the integral. Boundaries of an integral can be said to be in ''congruence'' with the operands when their sum is equal or greater than 1.

 

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. Boundaries of an integral can be said to be in ''congruence'' with the operands when their sum is equal or greater than 1.

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.

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 is the inverse function of [[derivative|derivation]], and is related to it by the [[Fundamental Theorem of Calculus]].

Integration is the inverse function of [[derivative|derivation]], and is related to it by the [[Fundamental Theorem of Calculus]].

[[Category:Calculus]]

[[Category:Calculus]]

[[Category:Mathematics]]

[[Category:Mathematics]]