 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2017/paper-2/8/b/solution

Here

y = 0

, the unit normal vector is

e_{y}

, and

F \cdot e_{y} = x^{2}

. The square has

- 1/2 \leq x, z \leq 1/2

, so its outward flux is

\int_{- 1/2}^{1/2} \int_{- 1/2}^{1/2} x^{2} d x d z = \frac{1}{12} .

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