That cannot be the correct value because the cos 16x function undergoes 4 complete oscillations from 0 to pi/2. The average value must be zero.
The indefinite integral is (1/16)sin(16x).
Evaluate it at x = pi/2 and 0 and take the difference.
0 - 0 = 0
Divide by the interval (pi/2) and you still get zero for the average value.
Find the average value of the function on the given interval:
f(x)=cos(16x), [0,pi/2]
The answer I got is 1.
3 answers
I got that the first time, but I though something was wrong.
This is a problem that could have been answered by inspection. You have an integer number of oscillations about a mean value of zero.