Question
Find the center of gravity $(\bar{x}, \bar{y})$ of a mass of density $f(x, y)=1$ the the given region $R$$$R \text { the semidisk } x^{2}+y^{2} \leq a^{2}, y \geq 0$$
Step 1
Since the density $f(x, y) = 1$, the mass $m$ is equal to the area of the region $R$. The region $R$ is a semicircle with radius $a$, so its area is $\frac{1}{2}\pi a^2$. Therefore, the mass $m$ is $\frac{1}{2}\pi a^2$. Show more…
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