Verified answer

The average value of some function y = f(x) on the interval [a,b] is defined as:

1/(b - a)*∫f(x) dx from a to b

In this case:

Average value = 4/π * ∫cos(2x) dx from 0 to π/4 = 4/π *[1/2*sin(2x) eval. from 0 to π/4]

= 4/π*[1/2] = 2/π