A hydrology research team monitors the flow rate r(t) (in cubic meters per hour) of a river for the eight–hour interval 0≤t≤8. The value of the definite integral ∫08r(t)dt is denoted by V.
(a) Interpret the quantity ∫08r(t)dt in the context of the problem, including appropriate units.
(b) Let Favg represent the average flow rate of the river over the same interval. Explain why Favg must satisfy the relationship Favg(8)=V.
(c) Provide a reasoning‐based argument that there exists at least one time c∈[0,8] at which r(c)=Favg. Clearly state any theorem or principle you invoke in your argument.