 Solution

ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2010/d/d2/1/solution

Both functions are integrable on $(0, 1)$ . The oscillatory function is measurable and bounded by

1

\int_{0}^{1} h (x) d x = \int_{0}^{1} \frac{d x}{1 - x ^{2}} = \frac{π}{2} < \infty.

In particular its singularity at the right endpoint is of integrable inverse-square-root type.

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