In someone infected with measles, the virus level N (measured in number of infected cells per mL of blood plasma) reaches a peak density at about t = 12 days (when a rash appears) and then decreases fairly rapidly as a result of immune response. The area under the graph of Nstd from t = 0 to t = 12 (as shown in the figure) is equal to the total amount of infection needed to develop symptoms (measured in density of infected cells 3 time). The function N has been modeled by the functionUse this model with six subintervals and their midpoints to estimate the total amount of infection needed to develop symptoms of measles.

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f(t) = -t(t – 21)(t + 1)