The likelihood that a person with a contagious disease will infect others in a social situation may be assumed to be a function f(s) of the distance s between individuals. Suppose contagious individuals are uniformly distributed throughout a rectangular region R in the xy plane. Then the likelihood of infection for someone at the origin (0, 0) is proportional to the exposure index E, given by the double integral

where

is the distance between (0, 0) and (x, y). Find E for the case where

and R is the square R: −2 ≤ x ≤ 2, −2 ≤ y ≤ 2

Transcribed Image Text:

E = f(s) dA JR