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Integrate f(x,y) over a disk

I have a homogeneous polynomial $F(x,y)$, and I'd like to integrate it over a disk $B_1(0)$, or approximate by integrating over a regular polygon. I just need the numerical value or an approximation of $$\int_{B_1(0)}F(x,y)dxdy$$ I looked up everywhere but I can't seem to find a way to do it. I used

integral ( integral ( F , x , -1 , 1 ), y , -1 , 1 )

for integrating over a rectangle, but I couldn't even find a way to integrate over regular polygons, and such an approximation would suffice.

Is there a way to integrate directly over disks ?