A thin plate in the xy-plane occupies the smaller region cut from the ellipse x 2 + 2y 2 = 6 by the parabola x = 2y 2 . The density is given by (x,...

A thin plate in the xy-plane occupies the smaller region cut from the ellipse x 2 + 2y 2 = 6 by the parabola x = 2y 2 . The density is given by δ(x, y) = x + y. Find the center of mass of this plate and its moments of inertia about the origin