I've recently been reading a programming textbook that I've seen recommended to undergraduates. In it, the following approximation appears:
What is this approximation? It seems elementary enough to have a name, but I do not believe that I have encountered it before. In fact, I can't even recall having seen this notation.
To be clear, I just want to know what the name of this trick is. Once I've got that, I'm happy to do any further reading myself.
This is the "midpoint rule" approximate Riemann sum/"method of Riemann summation". Note that they are using $dx$ to stand for a small real number (usually denoted $h$ or $\Delta x$), rather than something more calculus-y.