Use a graphing utility to verify that the functions f(x) = sin kx have a period of 2π/k, where k = 1, 2, 3, . . . Equivalently, the first “hump” of f(x) = sin kx occurs on the interval [0, π/k). Verify that the average value of the first hump of f(x) = sin kx is independent of k. What is the average value?