 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2005/paper-1/8/a/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

The positive integrand factors into three one-variable functions on a rectangular domain. Fubini's theorem therefore gives

(\int_{1}^{2} x^{- 2} d x) (\int_{1}^{2} y^{- 3} d y) (\int_{1}^{2} z^{- 4} d z) = \frac{1}{2} \frac{3}{8} \frac{7}{24} = \frac{7}{128} .

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