Mathematics

Problem

Consider

f(x)=\sin x

on the interval

[0,\pi]

. Let

\bar f_1

be its average value on

[0,\pi/2]

and

\bar f_2

be its average value on

[\pi/2,\pi]

. Which of the following is correct? a)

\bar f_1>\bar f_2

\bar f_1+\bar f_2=1

\bar f_1=\bar f_2

\bar f_1+\bar f_2=\dfrac{2}{\pi}