 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2009/paper-2/2/i/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

x^{2} sin x

is an odd function, since

x^{2}

is even and the sine is odd. Its integral on the symmetric interval therefore cancels:

\int_{- π}^{π} x^{2} sin x d x = 0.

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