The rate at which urban dogs are infected by a highly contagious ringworm outbreak is approximated by D(t) = 12.73*t*e^-0.3t, where D(t) is measured in dogs per month and t is in months since the outbreak which occurred on March 1.

In which month and what rate is the ringworm outbreak at its maximum? Explains your results completely and then find how many dogs, total were infected during this outbreak? (Use Integrals)