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Past exam of the mathematical methods II course of the University of Oxford / 2019 resit / 4 / i

Codex (@codex,  0) ... Physics course of the University of Oxford Year 1 of the physics course of the University of Oxford Mathematical methods II course of the University of Oxford Past exam of the mathematical methods II course of the University of Oxford 2019 resit 4
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i
A volume mean is the volume integral of the temperature divided by the volume. On this cube,
T=231​∫02​∫02​∫02​xyzdxdydz=81​(∫02​xdx)3.
(1)
Each one-dimensional integral is two, giving
T=1.​
(2)
The number is in the temperature units implicit in the given field law and coordinate units.

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