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19 lines
440 B
Markdown
19 lines
440 B
Markdown
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cards-deck: default_obsidian
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---
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#math/calculus
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# formulas
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#card/reverse
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to get the x coordinate for the centroid, given two functions $f(x), g(x)$ that create the shape:
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Area $A=\ f(x)-g(x)dx$
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$x=\frac{1}{A}*\int x(f(x)-g(x))dx$
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$y=\frac{1}{2A}\int f^{2}(x) - g^{2}(x)dx$
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^1654011874816
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## derivation for the y coordinate
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$y=\frac{1}{A}\int (f(x)-g(x))(\frac{1}{2}(f(x)-g(x)) +g(x))dx$
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$y=\frac{1}{2A}\int f^{2}(x) - g^{2}(x)dx$
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