Calculate I = ∫ (x + | y |) ds, where ∑ is the surface | x | + | y | + | Z | = 1 | Math enthusiast | Mathematical art

Calculate I = ∫ (x + | y |) ds, where ∑ is the surface | x | + | y | + | Z | = 1

First of all, Σ is symmetric with respect to x, y and Z, so I = ∫∫ (| y |) ds = 1 / 3 ∫∫ (| x | + | y | + | Z |) ds = 1 / 3 times the surface area of the regular octahedron. If the surface area of the regular octahedron is not calculated, please ask

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