Answer
$119in^4$
Work Step by Step
We can find the product of inertia of the shaded area with respect to the x and y axes as follows:
$I_{xy, whole}=\bar{I_{xy}}+A\bar{x}\bar{y}$
$\implies I_{xy, whole}=0+4(6)(3)(2)=144in^4$
Similarly $I_{xy, circle}=\bar{I_{xy}}+A\bar{x}\bar{y}$
$\implies I_{xy, circle}=0+\pi (1)^2(4)(2)=25.14in^4$
Now $I_{xy}=I_{xy, whole}-I_{xy, circle}$
We plug in the known values to obtain:
$I_{xy}=144-25.14=119in^4$
