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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

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