Integral calculus

Constant of integration

In calculus, the constant of integration, often denoted by , is a constant term added to an antiderivative of a function to indicate that the indefinite integral of (i.e., the set of all antiderivatives of ), on a connected domain, is only defined up to an additive constant. This constant expresses an ambiguity inherent in the construction of antiderivatives. More specifically, if a function is defined on an interval, and is an antiderivative of , then the set of all antiderivatives of is given by the functions , where is an arbitrary constant (meaning that any value of would make a valid antiderivative). For that reason, the indefinite integral is often written as , although the constant of integration might be sometimes omitted in lists of integrals for simplicity. (Wikipedia).

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Related pages

Differential operator | Vector space | Antiderivative | Derivative | Almost everywhere | Lists of integrals | Up to | Hyperplane | Initial condition | Connected space | Set (mathematics) | Real number | Locally constant function | Constant term | Initial value problem | Fundamental theorem of calculus | Cantor function | Calculus | Abstract algebra | Interval (mathematics) | Kernel (algebra) | Coset | Heaviside step function