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- Use numerical integration to find the centroid of the volume generated by revolving the area shown about the x-axis.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.Compute the centroidal coordinates of the L-shaped region in terms of b and t using the method of composite areas.