Definition:Primitive (Calculus)/Indefinite Integral

From ProofWiki
Jump to: navigation, search

Definition

Suppose that the real or complex function $F$ is a primitive of the function $f$.


From the Fundamental Theorem of Calculus, it is apparent that to find the value of a definite integral for a function between two points, one can find the value of the primitive of the function at those points and subtract one from the other.

Thus arises the notation:

$\displaystyle \int f \left({x}\right) \ \mathrm d x = F \left({x}\right) + C$

where $C$ is the arbitrary constant.


In this context, the expression $\displaystyle \int f \left({x}\right) \ \mathrm d x$ is known as the indefinite integral of $f$.


Sources