Consider a two dimensional lamina with constant density occupying the "deformed rect- angle" in the x-y plane shown in the following diagram, with q≥ 0. Y y = q(1-r²)+1 x=-1 x=1 y= q(1-x²) I Find the centre of mass of the lamina for arbitrary, non-negative q, and determine the range of values of q for which the centre of mass mass lies inside the region.