There are three formulas displayed in the quoted text below. Rewrite each of the three formulas in terms of area.
We actually answered that question in the distance-from-speed calculation, for which we already had a meaning for average speed. In fact, we know that
total distance traveled `=` (average speed) `times` (length of time interval),
or
average speed `=` (total distance traveled)/(length of time interval).
In our new language of integrals, the total distance is the definite integral of the speed function. Thus
average speed `= 1/(b-a)int_a^b vtext[(]t text[)] dt`.