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Let h(x) = x on (0,2 c) Suppose e > 0 Construct a partition Pe of (0, 2) so that U(h, P) – L(h, P) < € d) Use our definition of the Riemann integral, together with the fact that we know ſh exists, to prove that s'h=2.

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E } u v o } u u µ v Ç } o o p o p v u v Á z h x^ x ^ v µ } v e µ v p µ } v o z µ u v 0dlqh. WZ ^^ Z > ^ u o v ^ À = í ô ô ô ñ ô ô ð ñ ò ó ~ } o o ( W ( o v ^ À = ô ñ î î ô ð ð õ ï ï ï. Proof that 9x(P(x) _Q(x)) (= 9xP(x) _9xQ(x) Suppose 9xP(x) _9xQ(x) Breaking up by cases, if 9xP(x) is true (case 1), then P(c) is true for some c, and thus P(c) _Q(c) is true for that c If 9xQ(x) is true (case 2), then Q(d) is true for some d, and thus P(d) _Q(d) is true for that d In either case 9x(P(x) _Q(x)) is true.

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