8.3 Applications of Integral Calculus by SGLee - HSKim, JYLee, JHLee
1. Find the center of mass of the region bounded by the cycloid below and axis
(we assume that the density of the enclosed region is 1).
By the symmetry principle, the center of mass must lie on the axis, so . The area of the region is computed as follows:
Therefore, recalling the formula for -coordinate of the center of mass is given as follows:
Summing up, the center of mass is
2. By using graphical tools, find the approximate center of mass of the region
which is bounded by the , .
By looking at the figure it is clear that the center of mass of the region approximately .