 Solution

ID: past-exam-of-the-probability-statistics-and-options-ii-course-of-the-university-of-oxford/2009/d/d3/ii/a/solution

(0, 1)

its absolute value is at most

x ∣ lo g x ∣

, which has integral

1/4

, by integration by parts or the substitution

x = e^{- t}

. The function is measurable and this majorant is integrable, so

x lo g x / (1 + x)^{2} is integrable on (0, 1)

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