We can extend our definition of average value of a continuous function to an infinite interval by defining the average value of f on the interval [a, ∞] to be




(a) Find the average value of y = tan€“1x on the interval [a, ∞].
(b) If f(x) > 0 and ∫∞ f(x) dx is divergent, show that the average value of f on the interval [a, ∞] is limx →∞ f(x), if this limit exists.
(c) If ∫∞ f(x) dx is convergent, what is the average value of f on the interval [a, ∞]?
(d) Find the average value of on the interval [a, ∞].

Transcribed Image Text:

lim f- a Ja (x) dx -x