Constant of integration

In calculus, the constant of integration, often denoted by (or ), 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.[1][2][3] 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 [4] although the constant of integration might be sometimes omitted in lists of integrals for simplicity.

  1. ^ Stewart, James (2008). Calculus: Early Transcendentals (6th ed.). Brooks/Cole. ISBN 0-495-01166-5.
  2. ^ Larson, Ron; Edwards, Bruce H. (2009). Calculus (9th ed.). Brooks/Cole. ISBN 0-547-16702-4.
  3. ^ "Definition of constant of integration | Dictionary.com". www.dictionary.com. Retrieved 2020-08-14.
  4. ^ Weisstein, Eric W. "Constant of Integration". mathworld.wolfram.com. Retrieved 2020-08-14.