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cards-deck: default_obsidian
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#math/calculus 

# formulas
#card/reverse 
to get the x coordinate for the centroid, given two functions $f(x), g(x)$ that create the shape:
Area $A=\ f(x)-g(x)dx$
$x=\frac{1}{A}*\int x(f(x)-g(x))dx$
$y=\frac{1}{2A}\int f^{2}(x) - g^{2}(x)dx$
^1654011874816

## derivation for the y coordinate
$y=\frac{1}{A}\int (f(x)-g(x))(\frac{1}{2}(f(x)-g(x)) +g(x))dx$
$y=\frac{1}{2A}\int f^{2}(x) - g^{2}(x)dx$