Chapter 14.8, Problem 31ES

Use the numerical triple integral capability of a CAS approximate the location of the centroid of the solid that is bounded above by the surface $z=1/\left(1+x^2+y^2\right),$ below by the xy-plane, and laterally by the plane $y=0$ and the surface $y=\sin x\text{for 0}\le x\le \pi$ (see the accompanying the figure on the next page.