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Lecture Notes 3

# Lecture Notes 3 - 5.3 The Definite Integral When the...

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5.3 The Definite Integral When the definition is satisfied, we say the Riemann sums of f on [a, b] converge to the definite integral g G ± ²³´µ¶´ · ¸ and that f is integrable over [a, b]. Ex 1 Express the limit as a definite integral: lim ||¹||º» ½ ¾ ∆´ ½ ¿ ½ÀÁ , where P is a partition of [-1, 0]

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Ex 2 Suppose that f and g are integrable and that g G±²³´² µ ¶1, g G±²³´² µ 5, · ¸ · ¹ g º±²³´² µ 4 · ¸ Find: a) g ¶2G±²³´² · ¸ b) g »G±²³ ¼ º±²³½´² · ¸ c) g »2G±²³ ¶ 3º±²³½´² · ¸ d) g G±²³´² ¹ · e) g G±²³´² ¸ ¹ f) g »º±²³ ¶ G±²³½´²

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