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Please explain Improper Integrals. Say that f is integrable on [a, .) if lim fo f(x) dx =: fo f(x) dx exists. b-+0o (a) For

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Improper Integrals. Say that f is integrable on [a, .) if lim fo f(x) dx =: fo f(x) dx exists. b-+0o (a) For which real values of p does fe coo (logx) dx exist? X (b) Show that So sink dx exists. HINT: Consider the alternating series Enzo nn (n+1)a sinx dx. X X

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