 Solution

ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2008/d/d2/b/i/solution

The function is measurable and

0 \leq cos^{2} (1/ x) \leq 1

. The interval has finite measure, so its integral is at most one. Hence it is integrable, despite its oscillations near zero.

 New to topics? Read the docs here!