Antiderivatives and Indefinite Integrals
Definition
A function $F$ is called an antiderivative of another function $f$ if it satisfies $F^{\prime} = f$.
Explanation
An antiderivative is translated as 원시함수 (primitive function), 역도함수 (reverse derivative), etc.
The process of finding a function $F$ that satisfies $F^{\prime} = f$ for a given $f$, or the function $F$ itself, is called an indefinite integral. The indefinite integral or antiderivative of $f$ is expressed as follows:
$$ \int f(x)dx $$
Since a constant differentiated becomes $0$, if a function $F$ is an indefinite integral of $f$, then $F + C$ is also an indefinite integral of $f$ for any arbitrary constant $C$. In other words, there are infinitely many indefinite integrals for a given function. Thus, when expressing an indefinite integral, it is written as follows:
$$ \int f(x)dx = F(x) + C $$