 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-1/3/b/solution

ln ∣ x ∣

, valid on either half-line away from zero:

\int_{- 2}^{- 1} \frac{d x}{x} = [ln ∣ x ∣]_{- 2}^{- 1} = ln 1 - ln 2 = - ln 2 .

The negative answer is consistent with a negative integrand and increasing integration limits.

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