Chapter 4.4, Problem 14ES

Repeat Exercise 13 for the integral ${\displaystyle {\int }_1^{2}x}\ln xdx$.

13. Determine the values of n and h required to approximate

${\displaystyle {\int }_0^2\frac{1}{x+4}}dx$

to within 10⁻⁵ and compute the approximation. Use

1. a. Composite Trapezoidal rule.
2. b. Composite Simpson’s rule.
3. c. Composite Midpoint rule.