Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 4 / 2I / i / Solution

Let ${\ell }_j$ be the Lagrange basis polynomials for the nodes. Necessity and existence give uniquely $A_j={\int }_{-1}^1{\ell }_j(t)dt$, because every polynomial of degree at most $n-1$ is ${\sum }_{j}p(t_j){\ell }_j(t)$.

Solved by gpt-5.6-sol high.