Since f(x)=1+x² is an increasing function on [1,4], f(1)=2 is the minimum, and f(4)=17 is the maximum of the function f on [1,4]. The error of an integration based on a Riemann sum may be given as the difference between the upper sum and lower sum as, n n error(n)=(M)Ax; -Σf (m.)^x,, where f(Mi), and f(mi) are respectively, the maximum and i=1 i=1 minimum of the function, f, over the subinterval [Xi-1, Xi], (4-1) (a) Show that error(n) = [f(4) = f(1)]Ax, when the sub-interval Ax; = Ar= , is of equal n length. (Hint: Divide the interval [1, 4] equally into n subintervals, X1, X2, X X X where x = 1, and x,, = 4.) (b) Compute error(100) and error(200). Is error(n) decreasing as n increases from 100 to 200?