§15.6 Applications

Masses and moments

Examples

1. Find the centroid of the region bounded by $y=0$ and $y=2\sin(x),\ 0\le x\le\pi$.
2. Find the center of mass of the square plate \[\{0\le x\le\tfrac\pi2,\, 0\le y\le\tfrac\pi2\}\] with density $\delta(x,y)=2+\cos(x+y)$.
3. Find the moment of intertia with respect to the \(y\)-axis of a thin plate of constant density $\delta=1\text{ g/cm}^2$ bounded by the curve $y=\frac{\sin^2x}{x^2}$ and $\pi\le x\le2\pi$.