The age specific death rate for the member of a particular s

The age -specific death rate for the member of a particular stationary population is given by Find the mean age of members of the population.

Solution

h(X) = 1/(90-x) 0<=x<=90
Mean = integral x/(90-x) dx = -x-90 log(90-x)+constant
As x lies b/w o to 90 = [ -x-90 log(90-x) ] ~ [ 0,90 ]
                   = [(-90-90*log 0 ) - (- 0 - 90 log 90) ]
                   = [ -90 - 90 log 0 + 0 + 90 log 90 ]
                   = [ -90 + 175.88 ]
                   = 85.88