Chapter 7.7, Problem 37E

Trapezoid Rule and Simpson’s Rule Consider the following integrals and the given values of n.

1. a. Find the Trapezoid Rule approximations to the integral using n and 2n subintervals.
2. b. Find the Simpson’s Rule approximation to the integral using 2n subintervals. It is easiest to obtain Simpson’s Rule approximations from the Trapezoid Rule approximations, as in Example 7.
3. c. Compute the absolute errors in the Trapezoid Rule and Simpson’s Rule with 2n subintervals.

37. ${\displaystyle {\int }_1^e\frac{dx}{x}}$; n = 50