# Who introduced the term indefinite integral and the notation $\int f(x)dx$?

I find the notation $\int f(x)dx$ for the indefinite integral of $f(x)$ on some interval $I$ is both suggestive and confusing. On the one hand, this notation is very suggestive when we calculate the indefinite integral either by the change of variable formula or the integration by parts formula. On the other hand, this notation looks very likely with the definite integral notation $\int_a^b f(x)dx$. But these two terms arise from different backgrounds, one to find the primitive while the other to find the area.

I want to know who introduced the term indefinite integral and the notation $\int f(x)dx$ and why?

• Good question; you may want to check out History of Science and Mathematics in case it's already answered there. – user147263 Dec 15 '14 at 3:24
• I believe Leibniz. Recall the definition of the definite integral, taking the limit of Riemann sums. Change $\lim \sum$ to $\int$, $f(x_i ^*)$ to $f(x)$, and $\Delta x$ to $dx$, and there you go! (Note that $\int$ is like an elongated S, for "sum"... – Forever Mozart Dec 15 '14 at 3:28
• This is a good question, but for History of Math and Science Stack Exchange. – Mark Fantini Dec 15 '14 at 3:32

Notation was introduced by Leibniz..Earlier he used $\overline{omn} l$ where omn stands for sum and $l$ for differences.Later he used $\int$ for $\overline{omn}$. It was elongated S from sum.