 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2006/paper-2/3/a/i/solution

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

Integrating the first component with respect to

x

suggests

ϕ = x y + g (y, z)

. Matching the other components gives

g = sin (yz) + C

. Direct differentiation verifies

ϕ_{1} = x y + sin (yz) + C, F_{1} = \nabla ϕ_{1} .

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