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).

   , , 

   (Hint: )

    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 , .

            http://matrix.skku.ac.kr/cal-lab/cal-8-3-3.html 

 By looking at the figure it is clear that the center of mass of the region approximately .

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