Difference between revisions of "Antiderivative"
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| − | In [[calculus]], an '''antiderivative''' (or primitive function, primitive integral, indefinite integral, etc.) of a [[Function (mathematics)|mathematical function]] <code>f</code> is a differentiable function <code>F</code | + | In [[calculus]], an '''antiderivative''' (or primitive function, primitive integral, indefinite integral, etc.) of a [[Function (mathematics)|mathematical function]] <code>f</code> is a differentiable function <code>F</code> whose derivative is equal to the original function <code>f</code>. |
This can be stated symbolically as <code>F′ = f</code>. | This can be stated symbolically as <code>F′ = f</code>. | ||
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* [[Calculus]] | * [[Calculus]] | ||
| + | * [[Constant of integration]] | ||
* [[Function (mathematics)]] | * [[Function (mathematics)]] | ||
* [[Mathematics]] | * [[Mathematics]] | ||
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* [https://en.wikipedia.org/wiki/Antiderivative Antiderivative] @ Wikipedia | * [https://en.wikipedia.org/wiki/Antiderivative Antiderivative] @ Wikipedia | ||
| + | [[Category:Mathematics]] | ||
Latest revision as of 07:00, 17 March 2016
In calculus, an antiderivative (or primitive function, primitive integral, indefinite integral, etc.) of a mathematical function f is a differentiable function F whose derivative is equal to the original function f.
This can be stated symbolically as F′ = f.
Contents
Description
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.
Relationship to definite integrals
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.
Antidifference
The discrete equivalent of the notion of antiderivative is antidifference.
See also
External links
- Antiderivative @ Wikipedia
