Chapter 8.8, Problem 55E

Comparing the Midpoint and Trapezoid Rules Compare the errors in the Midpoint and Trapezoid Rules with n = 4, 8, 16, and 32 subintervals when they are applied to the following integrals (with their exact values given).

45. ${\displaystyle {\int }_0^{\pi /2}{\cos }^{9}xdx=\frac{128}{315}}$