Find the average value of the function f ( x ) = 3 cos 3 x + 2 cos 2 x {\displaystyle f(x)=3\cos ^{3}x+2\cos ^{2}x} on the interval 0 ≤ x ≤ π 2 {\displaystyle 0\leq x\leq {\frac {\pi }{2}}} . Simplify your answer completely.
