Definition:Primitive (Calculus)/Real

Definition
Let $F$ be a real function which is continuous on the closed interval $\closedint a b$ and differentiable on the open interval $\openint a b$.

Let $f$ be a real function which is continuous on the open interval $\openint a b$.

Let:
 * $\forall x \in \openint a b: \map {F'} x = \map f x$

where $F'$ denotes the derivative of $F$ with respect to $x$.

Then $F$ is a primitive of $f$, and is denoted:
 * $\displaystyle F = \int \map f x \rd x$

Also known as
A primitive is also known as an antiderivative.

The term indefinite integral is also popular.