Chapter 22, Problem 2P

Use Romberg integration to evaluate

$I={\displaystyle {\int }_1^2{\left(x+\frac{1}{x}\right)}^2}dx$

to an accuracy of ${\epsilon }_s=0.5\%$ based on Eq. (22.9). Your results should be presented in the form of Fig. 22.3. Use the analytical solution of the integral to determine the percent relative error of the result obtained with Romberg integration. Check that ${\epsilon }_t$ is less than the stopping criterion ${\epsilon }_s$.