Question

Find the average value of the function on the given interval:

f(x)=cos(16x), [0,pi/2]

The answer I got is 1.

Answer 1

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.

Answer 2

I got that the first time, but I though something was wrong.

Answer 3

This is a problem that could have been answered by inspection. You have an integer number of oscillations about a mean value of zero.