Chapter 14.4, Problem 20E

Finding the Center of Mass In Exercises 11–22, find the mass and center of mass of the lamina bounded by the graphs of the equations for the given density. (Hint: Some of the integrals are simpler in polar coordinates.)

$y=\cos \frac{\pi x}{L}$, $y=0$, $x=0$, $x=\frac{L}{2}$, $\rho =ky$

Finding the Center of Mass In Exercises 11–22, find the mass and center of mass of the lamina bounded by the graphs of the equations for the given density. (Hint: Some of the integrals are simpler in polar coordinates.)

$y=\cos \frac{\pi x}{L}$, $y=0$, $x=0$, $x=\frac{L}{2}$, $\rho =ky$