quartz/content/Obsidian Vault/centroids.md

cards-deck
default_obsidian

#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