In calculus, an antiderivative, inverse derivative, primitive function,
primitive integral or indefinite integral[Note 1] of a function f is a
differentiable function F whose derivative is equal to the original function f.
This can be stated symbolically as F' = f.[1][2] 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 often denoted by capital Roman letters
such as F and G.[3]
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.
In physics, antiderivatives arise in the context of rectilinear motion (e.g., in
explaining the relationship between position, velocity and acceleration).[4] The
discrete equivalent of the notion of antiderivative is antidifference.
Contents
1
Examples
2
Uses and properties
3
Techniques of integration
4
Of non-continuous functions
4.1
Some examples
5
See also
6
Notes
7
References
8
Further reading
9
External links
Examples