3-8. Consider a particle to be constrained to lie along a one-dimensional segment 0 to a. We will learn in the next chapter that the probability that the particle is found to lie between I and x + dx is given by p(.r)dx : 3 sin2 wait a a where n = 1. 2, 3. . . . . First show that p(.r) is normalized New Show that the average position of the particle along the line segment is ail Is this result physically reasonable? The integrals that you need are (The CRC Handbook of Chemistry and Physics or The CRC Standaid Mathematical Tables; CRC Press: Boea Rnton, FL) . .t: sin 2a.: f 5an exit = E 4a and . 3 x2 x sin 2w\" cos 2a.: .rsm exdx=I- 4:: 8oz