Iterated limits for a paraboloid solid

If the volume of the region bounded by the paraboloid $z=x^{2}+y^{2}$ and the plane $z=2y$ is given by $$\int_{0}^{\alpha}\int_{\beta(y)}^{2y}\int_{-\sqrt{z-y^{2}}}^{\sqrt{z-y^{2}}}dx\,dz\,dy$$ then