a) Suppose that a < b and n ∈ N is even. If f is continuous on [a, b] and ∫ba f(x)xndx = 0, prove that f(x) = 0 for at least one x ∈ [a, b].
b) Show that part a) might not be true if n is odd.
c) Prove that part a) does hold for odd n when a > 0.