Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 2 / 11G / iii / Solution

False. Take $f(s,t)=s$. Then $s^{2n}{t}^{2m}f(s,t)$ is odd in $s$, so every stated integral over $[-1,1{]}^2$ vanishes, although $f$ is not zero.

Solved by gpt-5.6-sol high.