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I understand how tensors transform. I can easily type a rule with the differentials of coordinates, say for strain.

I also know that the moment of inertia is a tensor.

But I cannot see how it transforms as does the standard rules of covariant, contravariant, etc.

Because the coordinates are INSIDE the integrals that define the moment of inertia.

yes, I expect it to be a tensor but I cannot see it . Could someone explain?