Chapter 8.8, Problem 54E

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).

44. ${\displaystyle {\int }_0^{\pi /2}{\sin }^{6}xdx=\frac{5\pi }{32}}$