TITLE: Addition is to Integration as Multiplication is to ______
QUESTION [44 upvotes]: Addition is to Integration as Multiplication is to ______ ? Everyone knows that definite integration  is "a way to sum continuum-many terms" in a rough sense. Can we "multiply continuum-many factors"  in a similar sense?

REPLY [2 votes]: Product Integral. Math With Bad Drawings has an article that mentions it.
I think the one presented by Jim Belk is only Type I. Here is Type II.