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Unformatted text preview: which the integral converges and
evaluate the integral for those values of p. 57. y 59. y s 1
xp 1 0
1 58. 1
x ln x y e p s s y ys R s 2r
x r dr
sr 2 s 2 If the actual density of stars in a cluster is x r
ﬁnd the perceived density y s . dx 1
2 R r 2, 67. A manufacturer of lightbulbs wants to produce bulbs that last x p ln x d x 0 539 a photograph. Suppose that in a spherical cluster of radius R
the density of stars depends only on the distance r from the
center of the cluster. If the perceived star density is given by
y s , where s is the observed planar distance from the center of
the cluster, and x r is the actual density, it can be shown that dx 4 ❙❙❙❙ s s s s s s s s 60. (a) Evaluate the integral x0 x ne x d x for n 0, 1, 2, and 3.
(b) Guess the value of x0 x ne x d x when...
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- Fall '07