 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-2/26i/b/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Put

h (x) = u_{+} (x) - u_{-} (x) .

Vertical slicing and Fubini's theorem give

A (Ω) = \int_{x_{0}}^{x_{1}} h (x) d x .

The vertical slice of

S_{L} (Ω)

(- h (x) /2, h (x) /2)

and has the same length

h (x)

. Therefore

A (S_{L} (Ω)) = \int_{x_{0}}^{x_{1}} h (x) d x = A (Ω) .

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