Show that if f (x) = px2 + qx + r is a quadratic polynomial, then S2 = b a f (x) dx. In
Chapter 7, Problem 60(choose chapter or problem)
Show that if f (x) = px2 + qx + r is a quadratic polynomial, then S2 = b a f (x) dx. In other words, show that b a f (x) dx = b a 6 y0 + 4y1 + y2 where y0 = f (a), y1 = f a + b 2 , and y2 = f (b). Hint: Show this first for f (x) = 1, x, x2 and use linearity. 61
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