Chapter 6.6, Problem 272E

For the following exercises, compute the center of mass $\left(\bar{x},\bar{y}\right)$ . Use symmetry to help locate the center of mass whenever possible.

272. $\rho =2$ for the region bounded by $y=\cos \left(x\right)$ , $y=-\cos \left(x\right)$ , $x=-\frac{\pi }{2}$ , and $x=\frac{\pi }{2}$