Why is "antiderivative" also known as "primitive"?

Question

If I had to guess, I would say that calling the antiderivative as primitive is of French origin.

Is one term more popular than the other?

Answer 1

At least in the United States, it seems that antiderivative is the more prevalent term although primitive does still get used.

It seems that primitive is commonly used abroad. While antiderivative, primitive, and indefinite integral are synonymous in the United States, other languages seem not to have any equivalent terms for antiderivative.

As others have pointed out here How common is the use of the term "primitive" to mean "antiderivative"?, some languages such as Dutch only use the term, primitive.

Answer 2

In Théorie des fonctions analytiques (1797), Lagrange develops calculus based on the series expansion of a function $f\,x$ ($= f(x)$ in today's notation), which he calls the fonction primitive: $$f(x+i) = f\,x + p\,i + q\,i^2 + r\, i^2 + \&c$$ The coefficients $p$, $q$, $r$ etc. will be functions of $x$, which Lagrange calls fonctions derivées, that is, derived functions or as they have come to be called in English, derivatives. The function $p$ is the first derivative, and we have $p=f'(x)$ in today's notation. (Note that $q$ is not the second derivative, even though it is called a fonction derivée.) The so-called primitive function $f$, which was the starting point and so came first, the root meaning of primitive (Lat. primus, first), is what we might call an antiderivative or integral of $p$.

Lagrange was very influential, and others following his lead, such as Cauchy, adopted his terms primitive and derivée. The basis for the names "primitive" and "derivative" is just their roles in deriving the derivative function from the primitive function.

There seem to be no books on books.google.com before 1900 that contain the term "antiderivative." The earliest reference there is, oddly enough, a course description in the catalog of Univ. Chicago for 1903/04. I wouldn't expect a term to be introduced in a course description, so it must go back farther than that.