Question

A lamina occupies the part of the disk x2 + y2 ≤ 4 in the first quadrant and the density at each point is given by the function ρ(x,y) = 4(x^2+y^2).

A. What is the total mass?

B. What is the moment about the x-axis?

C. What is the moment about the y-axis?

D. Where is the center of mass? ( ? , ? )

E. What is the moment of inertia about the origin?