 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2017/paper-1/1/a/solution

On the negative half-line, an antiderivative of

1/ x

ln ∣ x ∣

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

The negative sign agrees with the negative integrand throughout the interval.

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