Question 8.8: Use the multiple trapezoidal rule to determine how the error...

We know that the integral is I = π^{−1}. Figure 8.6 shows the value of the error as a function of the number of trapezoids. For the smallest values of n, we can get a non-monotonic dependence of the error on n because we use a small number of line segments to represent a continuously varying function. Once we reach a modest number of trapezoids, the error is already quite small. For example, we are underestimating the integral by only 0.03. The plot corresponds to 100 trapezoids, which produces an underestimate of only 8.5 × 10^{−5}.