91Ó°ÊÓ

A beam 10 meters long has density \(\sigma(x)=x^{2}\) at distance \(x\) from the left end of the beam. Find the center of mass \(\bar{x}\).

A beam 10 meters long has density \(\sigma(x)=\sin (\pi x / 10)\) at distance \(x\) from the left end of the beam. Find the center of mass \(\bar{x}\).

A thin plate lies in the region contained by \(y=x^{1 / 3}\) and the \(x\) -axis between \(x=0\) and \(x=1 .\) Find the centroid.