How can I find a centroid of a shape that is bound by certain known equations? Here is a picture of the Tesla body panel that I graphed in Desmos and of which I want to know the centroid.
2026-02-23 17:26:12.1771867572
How would I find the centroid of Tesla body panel graphed on Desmos?
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The half-area method mentioned in the comment does't find the centroid - see my answer to this question for reasons why.
The centroid $(\bar{x}, \bar{y})$ of a figure of constant density is found by picking an origin (it doesn't matter where), and calculating $\bar{x} = \dfrac{1}{A}\displaystyle\int x \cdot\text{height}(x)~dx$ and $\bar{y} = \dfrac{1}{A}\displaystyle\int y \cdot\text{width}(x)~dy$, where $A$ is the area of the figure breaking the areas of integration up as you need to work around the peculiarities of your boundary functions.