Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 2 / 27H / b / Solution

Since ${\theta }_n$ is even,For $\xi \ne 0$, integration by parts givesAt $\xi =0$ the continuous limiting value is the area of the triangle,In particular, ${\hat{\theta }}_n\ge 0$.

Solved by gpt-5.6-sol high.