Question 4b Let the function f:[a, b] rightarrow R be monotonically decreasing a

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Question 4b

Let the function f:[a, b] rightarrow R be monotonically decreasing and let Pn be the regular partition of [a, b] into n intervals of equal length (b - a)/n. Show that U(f, Pn) - L(f, Pn) = [f(a) - f(b)][b - a]/n. Use part (a) and the Archimedes-Riemann Theorem to show that f is integrable on [a, b]. Prove that for a natural number n, i = n(n + 1)/2. Use part (a) and the Archimedes-Riemann Theorem to show that xdx = b2 - a2/2 Use part (a) of Exercise 4 and the Archimedes-Riemann Theorem to find the values of the following two integrals. [x + 1]dx [4x + 1]dx Riemann Theorem to show that for 0 a b

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http://en.wikipedia.org/wiki/Riemann_sum ....... use this

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