Past exam of the options II course of the University of Oxford / 2012 / D / D3 / b

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- Solution b

Solution

On finite intervals the function is continuous, but

\int_{0}^{R} \frac{x}{1 + x ^{2}} d x = \frac{1}{2} lo g (1 + R^{2}) ⟶ \infty.

Consequently its nonnegative integral on the half-line is infinite: it is not integrable. The divergence occurs at infinity, not at the origin.

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