 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-4/25j/c/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

ψ_{ε} : A \to A

vol (A) = \int_{A} det D ψ_{ε} = (1 + ε^{2})^{- (n + 1) /2} \int_{A} det (I + ε D ϕ) .

Rearranging gives

\int_{A} det (I + ε D ϕ) = vol (A) (1 + ε^{2})^{(n + 1) /2} .

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