I'd like to know where I went wrong :

A lattice with constant density is on the region under the curve from to . Find the moments of inertia and .

My attempt : :

I realize that the region is an upper semi circle with radius .

, which mean that does not depend on the mass of the lattice!

I'm guessing that my error comes from the first step, that is . Should I replace by , so ?

If so, then I don't understand why I can't take as ...