Mnemonic for centroid of a bounded region The centroid of a region bounded by two curves is given by:
$ \bar{x} = \frac{1}{A}\int_a^b{x\left[f(x)-g(x)\right]dx} $
$ \bar{y} = \frac{1}{A}\int_a^b{\left[\frac{(f(x)+g(x)}{2}(f(x)-g(x))\right]dx} = \frac{1}{2A}\int_a^b{\left(f^2(x) - g^2(x)\right)dx}$
where A is just the area of that region.
But I have a terrible time remembering those formulas (when taken in conjunction with all of the other things that need to be remembered), and which which moment uses which formula. Does anybody know a good mnemonic to keep track of them?
Hopefully this isn't off topic. Thanks

The mnemonics are
$$\overline x=\frac1A\int\int_Rx\,dy\,dx$$
and
$$\overline y=\frac1A\int\int_Ry\,dy\,dx$$
where $R$ is the region and $A=\int\int_R1\,dy\,dx.$
