Antiderivative

In <a href="/facts/Calculus/MEmUTYoz">calculus</a>, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a <a href="/facts/Continuous_function/sKbl02pB">continuous function</a> f is a <a href="/facts/Differentiable_function/jQqTgLk1">differentiable function</a> F whose <a href="/facts/Derivative/7Ito70Dh">derivative</a> is equal to the original function f. This can be stated symbolically as 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 often denoted by capital <a href="/facts/Roman_letters/7EWeJjUV">Roman letters</a> such as F and G.
Antiderivatives are related to <a href="/facts/Integral/4PeM0mJc">definite integrals</a> through the <a href="/facts/Fundamental_theorem_of_calculus/pHeSGtUx">second fundamental theorem of calculus</a>: the definite integral of a function over a <a href="/facts/Interval_(mathematics)/e9se3vTe">closed interval</a> where the function is Riemann integrable is equal to the difference between the values of an antiderivative evaluated at the endpoints of the interval.
In <a href="/facts/Physics/a7aH2y08">physics</a>, antiderivatives arise in the context of <a href="/facts/Rectilinear_motion/Vom0QwWe">rectilinear motion</a> (e.g., in explaining the relationship between <a href="/facts/Position_(physics)/Tpk5d9f2">position</a>, <a href="/facts/Velocity_(physics)/Q3o1LVDe">velocity</a> and <a href="/facts/Acceleration_(physics)/UVDmjYvR">acceleration</a>). The <a href="/facts/Discrete_mathematics/XdRUnzUL">discrete</a> equivalent of the notion of antiderivative is <a href="/facts/Antidifference/9sDo2RaR">antidifference</a>.

Antiderivative open-in-new

Antiderivative