 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2017/paper-2/16/b/iv/solution

The two independently computed answers agree:

\oint_{S} F \cdot n d S = \int_{V} \nabla \cdot F d V = - \frac{44}{3} .

This verifies the divergence theorem. Its hypotheses hold because the field is smooth and the prism has a closed piecewise smooth boundary with consistently outward normals.

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