# Antiderivative

In calculus, an antiderivative, primitive integral or indefinite integral of a function f is a differentiable function F whose derivative is equal to f, i.e., F ′ = f. The process of solving for antiderivatives is called antidifferentiation (or indefinite integration) and its opposite operation is called differentiation, which is the process of finding a derivative. Antiderivatives are related to definite integrals through the fundamental theorem of calculus: the definite integral of a function over an interval is equal to the difference between the values of an antiderivative evaluated at the endpoints of the interval.

The discrete equivalent of the notion of antiderivative is antidifference.

### Other articles related to "antiderivative, antiderivatives":

Riemann–Liouville Integral
... The integral is a manner of generalization of the repeated antiderivative of ƒ in the sense that for positive integer values of α, Iαƒ is an iterated antiderivative of ƒ of order α ... Clearly I1ƒ is an antiderivative of ƒ (of first order), and for positive integer values of α, Iαƒ is an antiderivative of order α by Cauchy formula for repeated integration ...
Antiderivative (complex Analysis) - Uniqueness
... Therefore, any constant is an antiderivative of the zero function ... If is a connected set, then the constants are the only antiderivatives of the zero function ... Otherwise, a function is an antiderivative of the zero function if and only if it is constant on each connected component of (those constants need not be equal) ...
Antiderivatives of Non-continuous Functions - Some Examples
... The function with is not continuous at but has the antiderivative with ... and is only discontinuous at 0, the antiderivative F may be obtained by integration ... The function with is not continuous at but has the antiderivative with ...
Antiderivative (complex Analysis) - Existence - Sufficiency
... of over any path depends only on the endpoints, then g has an antiderivative ... is connected, as otherwise one can prove the existence of an antiderivative on each connected component ... That this is an antiderivative of can be argued in the same way as the real case ...
Jackson Integral As Q-antiderivative
... Just as the ordinary antiderivative of a continuous function can be represented by its Riemann integral, it is possible to show that the Jackson integral gives a unique q-antiderivative within a certain ...