Consider a thin plate occupying the region D located in the upper half-plane (where y ≥0) and between the parabolas of equations y = 2- x² and y = 1-2x². The density of the plate is proportional to the distance from the x-axis.

a) Calculate the moments of inertia (second moments) of the plate with respect to the coordinate axes.

b) Is it easier to rotate the plate around the x-axis or the y-axis? Justify your answer. Here the calculations are simple, but long, so you can use a software to evaluate the integrals. You However, you must show the main steps of the calculation and give an exact answer.