Discussion on: 821 Rectangle minus semi-circle | Moment of Inertia

You can do integration, it is more convenient:
$\displaystyle I_y = \int x^2 \, dA = \int_{x_1}^{x_2} x^2 \, (y \, dx)$

$\displaystyle I_y = \int_0^8 x^2\left( 10 - \sqrt{8x - x^2} \right) \, dx$