 Solution

ID: past-exam-of-the-mathematical-methods-ii-course-of-the-university-of-oxford/2019-resit/4/i/solution

\overline{T} = \frac{1}{2 ^{3}} \int_{0}^{2} \int_{0}^{2} \int_{0}^{2} x yz d x d y d z = \frac{1}{8} (\int_{0}^{2} x d x)^{3} .

Each one-dimensional integral is two, giving

\overline{T} = 1.

The number is in the temperature units implicit in the given field law and coordinate units.

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