Which of the functions given below has an average (mean) value of zero on the interval - a=x=a, a>0? a. abs (x) b. cos (x) c. e^x d. sin (x) e. x^2+x^3

Odd functions have the property that the average on the interval [-a, a] is zero, because of this:

The definition of the average of a differentiable function is:

Average = { ∫ f (x) dx from - a to a } / [ a - (-a) ]

And for an odd fuction ∫f (x) dx from - a to a is zero = > Average = 0

The only odd function in the list is cos (x), then the answer is b. cos (x).