Problem 3 [6 points] 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 Mt) from 1': 0 to t=12 (as shown in Figure 2) is equal to the total amount of infection needed to develop symptoms (measured in density of infected cells x 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. N N = fl!) 1000 0 12 21 rmays) Figure 2 Problem 4 [6 points] (a) For f (x) = x2 as shown in Figure 3, evaluate the Riemann sums y = x2 0 Figure 3 (b) We can approximate the area under the graph of the function f (x) = x2 in (a) by n rectangles, each of width 1 as follows: Ax = - b-a 1-0 1 n n n Set Xo = 0, X1 = -, X2 = 2 , ... , Xi = ~, Xn = 1 EtzIf(x;) 4x, where f(x;) = (;) Show that the Riemann sum of the integral is 6 (1 + 1 ) ( 2 + 2 ) by using the formula 12 + 22 + ... + n2 = = n(n+ 1)(2n+ 1) (c) Find the area of the region by taking n - co