05:49
Calculus Early Transcendentals 2
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 $N(t)$ 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 $\times$ time). The function $N$ has been
modeled by the function
$$
f(t)=-t(t-21)(t+1)
$$
Use this model with six subintervals and their midpoints
to estimate the total amount of infection needed to develop
symptoms of measles.