Chapter 9, Problem 65P

Determine the centroidal coordinates of the plane region by numerical integration.

Use numerical integration to locate the centroid of the symmetric plane

Use integration to find the centroidal coordinates for the volume obtained by revolving the area shown about the x-axis.

Use numerical integration to find the centroid of the volume generated by revolving the area shown about the x-axis.

The sheet metal trough has a uniform wall thickness. Determine the coordinates of its center of gravity.

Use integration to locate the centroid of the shaded region in terms of R and t. (b) Show that when t0 the result of part (a) agrees with that given in Table 8.2 for a quarter circular arc.

Solve Prob. 8.43 assuming that the area is revolved about the y-axis.

Show that every axis passing through the centroid of the equilateral triangle is a principal axis.

The picture board and its triangular supporting bracket form a composite surface. Calculate the height h of the support that minimizes the centroidal z-coordinate of the assembly.