Chapter 6.7, Problem 2QCE

A homogeneous lamina of mass $M$ and density $\delta$ occupies a region in the $xy\text{-plane}$ bounded by the graphs of $y=f\left(x\right),y=0,x=a$ , and $x=b$ , where $f$ is a nonnegative continuous function defined on an interval $\left[a,b\right]$ . The $x\text{-}$ coordinate of the center of gravity of the lamina is $M_y/M$ , where $M_y$ is called the $\text{\_\_\_\_\_\_\_\_}$ and is given by the integral $\text{\_\_\_\_\_\_\_\_}$ .