Consider the following step function.

u(x) =0x01x> 0

Calculate the average value ofu(x)

on[1, 1].

Is there a valuecin[1, 1]

such thatu(c)

attains the average? If not, why does the mean value theorem for integrals fail?

Yes,u(c) attains the average value atc= 0.

No, there is no such value ofcbecauseu(x) is not continuous on [1, 1].

Yes,u(c) attains the average value atc= 0.5.

Yes,u(c) attains the average value atc= 1.

No, there is no such value ofcbecauseu(x) is not integrable on [1, 1].