Question

find the average value of f(x) = (4-x^2)^(1/2) on [-2,2]

Answer 1

The average value of a (well-behaved) function on a closed interval [a,b] is
\[ \frac{1}{b-a} \int_a^b f(x) \ dx \]
So evaluate that expression for your interval and your function.

Answer 2

btw, this integral can be evaluated very quickly by thinking about it geometrically vs. algebraically.