Which step has the error $if$ any?

$m={\displaystyle \underset{0}{\overset{2\sqrt[\phantom{2}]{2}}{}}}{\displaystyle \underset{-\sqrt[\phantom{2}]{8-x^2}}{\overset{\sqrt[\phantom{2}]{8-x^2}}{}}}{\displaystyle \underset{-1}{\overset{2}{}}}\sqrt[\phantom{2}]{1+x^2+y^2}dzdydx$

step$1$ region $Dis$ hath $of$ a disk

$={\displaystyle \underset{-\frac{}{2}}{\overset{\frac{}{2}}{}}}{\displaystyle \underset{0}{\overset{2\sqrt[\phantom{2}]{2}}{}}}{\displaystyle \underset{-1}{\overset{2}{}}}\sqrt[\phantom{2}]{1+r^2}dz(rdrd)$

use cylindirical coords

$$ step$$ seperate each integral

$={\displaystyle \underset{-\frac{}{2}}{\overset{\frac{}{2}}{}}}d{\displaystyle \underset{0}{\overset{2\sqrt[\phantom{2}]{2}}{}}}r\sqrt[\phantom{2}]{1+r^2}dr{\displaystyle \underset{-1}{\overset{2}{}}}dx$

${\displaystyle \underset{\phantom{}}{\overset{\text{s}\text{t}\text{e}\text{p}3}{}}}{u}^{-\text{s}\text{u}\text{b}}$ for midd interral

$=(\frac{1}{2}(1+r^2{)}^{\frac{3}{2}}{|}_0^{2\sqrt[\phantom{2}]{2}})3$

darr stept

$\{$:$\frac{3}{2\text{s}\text{t}\text{e}\text{p}5}-{19}^{312}-1^{312})$

$=\frac{3}{2}(27-1)$

$=\frac{57en}{39}$

$=39$