p40_016 - L Z / 4 sin 2 y dy = 2 y 2 sin 2 y 4 / 4 = 0 ....

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16. We follow Sample Problem 40-3 in the presentation of this solution. The integration result quoted below is discussed in a little more detail in that Sample Problem. We note that the arguments of the sine functions used below are in radians. (a) The probability of detecting the particle in the region 0 x L 4 is µ 2 L ¶µ L π Z π/ 4 0 sin 2 ydy = 2 π µ y 2 sin 2 y 4 π/ 4 0 =0 . 091 . (b) As expected from symmetry, µ 2 L ¶µ
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Unformatted text preview: L Z / 4 sin 2 y dy = 2 y 2 sin 2 y 4 / 4 = 0 . 091 . (c) For the region L 4 x 3 L 4 , we obtain 2 L L Z 3 / 4 / 4 sin 2 y dy = 2 y 2 sin 2 y 4 3 / 4 / 4 = 0 . 82 which we could also have gotten by subtracting the results of part (a) and (b) from 1; that is, 1 2(0 . 091) = 0 . 82....
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