 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-4/2i/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Let

ℓ_{j}

be the Lagrange basis polynomials for the nodes. Necessity and existence give uniquely

A_{j} = \int_{- 1}^{1} ℓ_{j} (t) d t

, because every polynomial of degree at most

n - 1

\sum_{j} p (t_{j}) ℓ_{j} (t)

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