Find the limits of integration for $\iiint_Ef(x,y,z)dzdydx$ where $E$ is bounded by the paraboloid $x=4y^2 + 4z^2$ an the plane $x=4$
I understand that it forms a paraboloid along the x axis. If we draw it on the xy plane where $z = 0$, we find that $x = 4y^2$, which is a parabola along the x axis limited by the line $x=4$. $ \int_{-1}^1\int_{4y^2}^4\int f(x,y,z)\:dz\:dy\:dx $
If we view it along the z axis, the paraboloid forms a circle where $x=4$, such that $4 = 4y^2 + 4z^2$. Solving for $z$ we get: $z = \pm\sqrt{1-y^2}$
So the limits of integration I came up with were:
$ \int_{-1}^1\int_{4y^2}^4\int_{-\sqrt{1-y^2}}^{\sqrt{1-y^2}} f(x,y,z)\:dz\:dy\:dx $
Where did I go wrong?