$(3$ points$)$ Suppose that $Cis$ a simple closed curve $in$ the $xy-$plane that has positive

orientation and encloses the region $D.$ Show that the center $of$ mass $ofDis(\stackrel{}{x}\frac{,}{b}ar(y)),$ where

$\stackrel{}{x}=\frac{-1}{A}{\displaystyle \underset{C}{\overset{\phantom{}}{}}}xydx$ and $\frac{?}{\text{b}\text{a}\text{r}}(y)=\frac{-1}{2A}{\displaystyle \underset{C}{\overset{\phantom{}}{}}}{y}^{2}dx,$ where $Ais$ the area $ofD.$ You should think

$ofDas$ a thin metal plate with constant density.