 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2006/paper-2/3/b/ii/solution

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

On the first segment only

z

varies and

F_{z} = x^{2} y = 0

. On the second only

y

varies and

F_{y} = x^{2} z = 0

. On the last segment

y = z = π

0 + 0 + \int_{0}^{π} (2 π^{2} x + sin x) d x = π^{4} + 2.

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