 Solution

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

The function is measurable and negative on this interval. Its absolute value obeys

0 \leq \frac{- x l o g x}{( 1 + x ) ^{2}} \leq - x lo g x, \int_{0}^{1} - x lo g x d x = \frac{1}{4} .

x^{2} lo g x \to 0

at zero. The comparison test for integrals proves integrability.

 New to topics? Read the docs here!