Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 2 / 11H / f / Solution

Write $f=Q_{2n-1}+E_n$, where $Q_{2n-1}$ contains the terms through degree $2n-1$. On $[-1,1]$,The quadrature error of $Q_{2n-1}$ is zero. Bounding the integral and quadrature errors of $E_n$ separately, using positive weights with total $\int r$, gives exactly

Solved by gpt-5.6-sol high.