The definite (Riemann) integral of a function $f:D\subseteq\mathbb R\rightarrow\mathbb R$ from $a$ to $b$ is, by definition, the following limit : $$\int_a^bf(x)\,dx = \lim_{n\rightarrow\infty}\sum_{i=1}^nf(x_i)\Delta x$$ for a subdivision of the interval $[a,b]$ into $n$ subintervals of equal length $\Delta x$, with $x_i$ being an arbitrary value in the $i$-th subinterval. In a sense, an integral is like a "sum" of infinitely (and continuously) many line segments, although this is ambiguous since the value of the integral doesn't change if we modify a countable set of line segments, for example.
I was wondering if there was an operator defined like this : $$\lim_{n\rightarrow\infty}\prod_{i=1}^nf(x_i)\Delta x$$ possibly for a specific class of functions $f$ ?