Chapter 5.3, Problem 11P

The following notation is used in the problems: $M\text{ = mass}$, $\bar{x},\bar{y},\bar{z}=$ coordinates of center of mass (or centroid if the density is constant), $I=$ moment of inertia (about axis stated), $I_x,I_y,I_z=$ moments of inertia about x, y, z axes, $I_m=$ moment of inertia (about axis stated) through the center of mass.

Note: It is customary to give answers for $I,I_m,I_x$, etc., as multiples of M (for example, $I=\frac{1}{3}M{l}^2$).

A chain in the shape $y=x^2$ between $x=-1$ and $x=1$has density .

Find (a) $M$, (b) $\bar{x},\bar{y}$.