Exercise 19

Let $D$ be a half-disk lamina of radius 3 in quadrants IV and I, centered at the origin as in Activity. Assume the density at point $(x,y)$ is equal to $x$.

1. Before doing any calculations, what do you expect the $y$-coordinate of the center of mass to be? Why?

2. Set up iterated integral expressions which, if evaluated, will determine the exact center of mass of the lamina.

3. Use appropriate technology to evaluate the integrals to find the center of mass numerically.