 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2011/paper-1/2/solution

u = 3 - 2 x

, so

d u = - 2 d x

\int \frac{d x}{3 - 2 x} = - \frac{1}{2} ln ∣3 - 2 x ∣ + C .

The antiderivative is taken on either interval separated by

x = 3/2

. Differentiating verifies the sign and factor

- 1/2

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