■e Preview No. 1: Locate the centroid of the plane area shown. y -12 in.- n.— 21 in. 15 in. X
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- Use numerical integration to find the centroid of the volume generated by revolving the area shown about the x-axis.Using integration, locate the centroid of the area under the n-th order parabola in terms of b, h, and n (n is a positive integer). (b) Check the result of part (a) with Table 8.1 for the case n = 2.Compute the centroidal coordinates of the L-shaped region in terms of b and t using the method of composite areas.
- 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.By integration, find the centroid of the surface of the hemisphere. Compare your result With Table 8.4.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.