I am having trouble finding the bounds for $z$ in the domain $S$. Where $S$ lies in the first octant ($x,y,z ≥ 0$) between the two surfaces $z = x^2+y^2$ and $x^2+y^2+z^2=2$. I have drawn the domain in the $Oxy$ plane and found $S = \{0\le{x}\le{1},0\le{y}\le{\sqrt{2-x^2}}\}$. I understand that $z$ is always below the two surfaces, such that $z\le{x^2+y^2}$ and $z\le{2-x^2-y^2}$ but I am unsure as to how I would write this in terms of one bound to complete my domain and integrate.
Any help appreciated.
P.s. the integral is $I = \iiint_{S}zdxdydz $