 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/iii/solution

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

Integrating the first component and checking the remaining partial derivatives gives

ϕ_{3} = x^{2} yz - cos x + C, F_{3} = \nabla ϕ_{3} .

This explicit scalar potential proves that the field is conservative.

 New to topics? Read the docs here!