Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 1 / 24G / c / i / Solution

Since $V$ is simply connected, $g$ has a primitive $G_0$. On connected $U\cap V$, $G_0-F$ has zero derivative and is constant. Adjust that constant to obtain $G=F$ on the overlap, hence the required continuation.

Solved by gpt-5.6-sol high.