Find the limits of integration ly, uy, lx, ux, lz, uz (some of which will involve variables $x, y, z$) so that $$\int_{\text{ly}}^{\text{uy}} \int_{\text{lz}}^{\text{uz}} \int_{\text{lx}}^{\text{ux}} \,dx\,dz\,dy$$ represents the volume of the region in the first octant that is inside the paraboloid $y = x^{2}+2z^{2}$ and between the planes $y = 6$ and $y = 10.$
lx =
ux =
lz =
uz =
ly =
uy =