Astronomers use a technique called stellar stereography to determine the density of stars in a star cluster from the observed (two-dimensional) density that can be analyzed from
a photograph. Suppose that in a spherical cluster of radius R the density of stars depends only on the distance from the center of the cluster. If the perceived star density is given by y(s), where is the observed planar distance from the center of the cluster, and x(r) is the actual density, it can be shown that

If the actual density of stars in a cluster is x(r) = ½ (R €“ r) 2, find the perceived density

2r )- (" x(r) dr ()x.