What is the Transformation Rule for the Moment of Inertia Tensor?

[JTC]

(Forgive me if this is in the wrong spot)

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?

 

[Dr.D]

Do not worry about the integrands. The inertia tensor is simply a 3x3 matrix and it transforms accordingly.