The probability that a marked flea beetle, Phyllotreta cruciferae or Phyllotreta striolata, will be recaptured within a certain distance and time after release can be calculated from the probability density function

where t is the time (in hours) after release, x is the distance (in meters) from the release point that recaptures occur, L is the maximum distance from the release point that recaptures can occur, and D is the diffusion coefficient. If t = 12, L = 6, and D = 38.3, find the expected recapture distance.

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p(x, t) = e-x²/(4Dt) L Jo -u²/(4Dt) du