Antiderivative
A function F(x) is an antiderivative of a function f(x) if F'(x) = f(x) for all x in the domain of f. The process of finding an antiderivative is antidifferentiation.
In calculus, an antiderivative or indefinite integral of a function is a function whose derivative is equal to the original function. In other words, if F(x) is an antiderivative of f(x), then F'(x) = f(x).
To find an antiderivative, one can use integration techniques such as substitution or integration by parts. The indefinite integral of a function is represented by a symbol called the integral sign (∫), and is written as ∫f(x)dx, where f(x) is the integrand and dx indicates the variable of integration.
It is worth noting that the antiderivative of a function is not unique, as it can have a constant of integration added to it. For example, if F(x) is an antiderivative of f(x), then F(x) + C, where C is any constant, is also an antiderivative of f(x).
Antiderivatives are useful in many areas of mathematics, science, and engineering, including physics, statistics, and finance.
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