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Question: 529 let f ab r a xo...

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5.2.9. Let f : [a,b] → R, a = xo < xl < < Xn-b, and suppose that /(Ak+) exists and is finite for k = 0, l , . . . , n-1 and f(xr) exists and is finite for k = 1, . . . , n. Show that if f is continuous on each subinterval k-1, x), then f is integrable on [a, b] and rk f(x) dx = Σ I - f(x) dx.

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