(Cauchy-Schwarz Inequality) Prove that if f,g are real functions such that f, g € RI([a, b]) then fg, f2.g² € RI([a, b]) and (C - S) cb 2 ·b \/" fg dx * ≤ [" \fP³ dx < ["\f1² da [° 19³² da. a a

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