Concept

Constant of integration

Summary
In calculus, the constant of integration, often denoted by C (or c), is a constant term added to an antiderivative of a function f(x) to indicate that the indefinite integral of f(x) (i.e., the set of all antiderivatives of f(x)), 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 f(x) is defined on an interval, and F(x) is an antiderivative of f(x), then the set of all antiderivatives of f(x) is given by the functions F(x) + C, where C is an arbitrary constant (meaning that any value of C would make F(x) + C a valid antiderivative). For that reason, the indefinite integral is often written as \int f(x) , dx = F(x) + C, although the constant of integratio
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