#### Answer

$I_x=204.8in^4$

#### Work Step by Step

The required moment of inertia can be determined as follows:
$dA=xdy$
Given that $y^2=x$
$\implies dA=y^2 dy$
Now $I_x=\int y^2 dA$
$\implies I_x=\int _0^4 y^2 y^2 dy$
$\implies I_x=\int_0^4 y^4dy$
$\implies I_x=\frac{y^5}{5}|_0^4$
$\implies I_x=\frac{1024}{5}$
$\implies I_x=204.8in^4$