Integrating by parts, show that I n = 1 0 e x x n dx =
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Integrating by parts, show that In = ∫10 exxn dx = e -nIn-1, I0 = e - 1.
(a) Compute In, n = 0, · · ·, using 4S arithmetic, obtaining I8 = -3.906. Why is this nonsense? Why is the error so large?
(b) Experiment in (a) with the number of digits k > 4. As you increase k, will the first negative value n = N occur earlier or later? Find an empirical formula for N = N(k).
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