The density of a region bounded by $y = \sin(x)$ and $y = 0$ from $x = 0$ to $x = \frac{\pi}{2}$ is given by $\rho = \cos(x)$. Find the centroid.
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When $x = 0$, $u = 0$. When $x = \frac{\pi}{2}$, $u = 1$. $$M = \int_0^1 u du = \frac{1}{2} u^2 \Big|_0^1 = \frac{1}{2}$$ Show more…
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