> the concept illustrated in the last figure is known as trapezoidal integration
And, as a consequence, the concept they call "time-weighted average" is just called "mean value of a function", at least in my country.
Also "hyperfunction" seems to be a terrible name. Unless we're talking about mathematics where the term has very specific meaning, how exactly is it different in programming from any ordinary function? (Possibly an aggregate function in SQL, of course.)