 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ii/paper-4/37e/b/i/solution

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

Along the radial curve at fixed

t, θ, φ

, the spatial line element is

d S = 1 + 2 M / r d r

. To first order,

S = \int_{r_{1}}^{r_{2}} (1 + \frac{M}{r}) d r,

S = (r_{2} - r_{1}) + M lo g \frac{r _{2}}{r _{1}} .

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