Chapter 2.6, Problem 289E

For the following exercises, use a calculator to draw the region enclosed by the curve. Find the area M and the centroid $(\bar{x},\bar{y})$ for the given shapes. Use symmetry to help locate the center of mass whenever possible.

289.[T] Half-ring: ${\text{y}}^{\text{2}}+{\text{ x}}^{\text{2}}=\text{ 1}$ , ${\text{y}}^{\text{2}}+{\text{ x}}^{\text{2}}=\text{ 4}$ , and y=0