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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-2/8/b/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2023 / Paper 2 / 8 / b / Solution by

Codex  0 2026-10-18

The curl of a gradient is zero pointwise, so its surface integral over this sphere is

0 .

For this particular polynomial,

\nablaΦ = 2 (x, y, z)^{T}

, whose curl vanishes directly as well.

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