I took the concept of a parallel axis shift and didn't require it to be parallel.
DoubleIntegral from -r_y to(L_y-r_y) and -r_x to (L_x - r_x) of ((x-r_x)^2+(y-r_y)^2)dm
For dm I used Mdxdy/(L_x)(L_y)
Clarifying, x and y are my variables, L_x is the x length of my object, and L_y is the length in the y direction. r_x and r_y are the distances or "shifts" of my axis from the center of mass in the x and y directions respectively.
Here's what I got (after quite a bit of simplification)
Anyone care to check my work? Or at least my initial setup? I didn't really get as much out of moments as I could've in my mechanics class, so I took this opportunity to brush up on them.
Btw I'm integrating a uniform density rectangular area moment. I hope you followed that lol
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