Triple integral changing order of integration

Consider, but do not evaluate, the integral from -2 to 2, from 0 to 1/2 sqrt(4-x^2), from x^2+3y^2 to 4-y^2, of the integrand x^3+y^3, dz dy dx.
a: Describe and sketch the solid region of integration.
b: Rewrite the integral in the orders dz dx dy, dy dz dx and dx dy dz.