> If you need to get the area under a curve by breaking it into a billion tiny rectangles, so what, your computer will do that calculation in a second or two.

> If you need to get the area under a curve by breaking it into a billion tiny rectangles, so what, your computer will do that calculation in a second or two. That, too, is calculus. However, a closed-form solution will always be preferred—"a second or two" might be acceptable if you're only evaluating the function once, but it's clearly not good enough when you're applying it to a large data set. We may all be carrying around supercomputers in our pockets but we're still well short of the point where that kind of optimization wouldn't lead to a noticeable increase in both performance and (practical) functionality.