2. (The Cauchy-Schwarz Inequality for Integrals) Suppose that the functions f. g, f, g, and fg are integrable on the closed, bounded interval [a, b]. Prove that 8 (Hint: For each number, define p() = ftf-g]. Show that p(x) is a quadratic polynomial for which p(2) 0 for all and therefore that its discriminant is not positive.)