 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ia/paper-3/9a/c/solution

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

The curl is

(2 y - y^{2}, x, 0)

, so the field is not conservative. On

C

z = 1

and

d z = 0

\oint_{C} (3 x d x + y^{2} d y) = \oint_{C} d (\frac{3}{2} x^{2} + \frac{1}{3} y^{3}) = 0.

 New to topics? Read the docs here!