The shelf life, in days, for bottles of a certain prescribed medicine is a random variable having the density function shown below. Find the probability that a bottle of this medicine will have a shelf life of (a) at least 50 days; (b) anywhere from 30 to 60 days.

f(x) = [ 5000 \ (x + 50) ^{3 ,} x > 0

0, elsewhere

(a) the probability of a shelf life of at least 50 days is ?