#4. Please show neat and complete work.

4. Let f(x) = VR2 - x2 for R > 0. (a) Show that the graph of f is a semicircle. (b) Find the average value of f over [-R, R]. HINT: You'll need to interpret the integral as an area .. . (c) Interpret your answer to part (b) geometrically on the graph below: (0!R) y = avg. value (-R,O) (R,O)