Question: Show that if (x) = px 2 + qx + r is a quadratic polynomial, then S 2 = b a (x) dx. In

Show that if ƒ(x) = px2 + qx + r is a quadratic polynomial, then S2 = ∫ba ƒ(x) dx. In other words, show that

f f(x) dx =! b-a 6 -(yo+ 4y1 + y2)

; (a+b) where yo = f(a), y = f and y2 = f(b). Show this first for f(x) = 1, x, x and use linearity.

So f f(x) dx = ! b-a 6 -(yo+ 4y1 + y2)

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