 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ib/paper-2/3d/i/solution

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

Square the Fourier series, integrate, and use orthogonality; cross terms vanish. This gives

\int_{- 1}^{1} ∣ f ∣^{2} = a_{0}^{2} /2 + \sum_{n \geq 1} (a_{n}^{2} + b_{n}^{2})

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