Question

Let ${\displaystyle \underset{2}{\overset{5}{}}}\frac{1}{x-1}dx$

$($a$)$ Evaluate the integral using the Octave commands.

$[2]$

$($b$)$ Approximate the value of the integral using the trapezoidal and Simpson's rules with $10$ subintervals.

$[6]$

$($c$)$ Compute the absolute error in the approximation of the integral using both methods.

$[2]$

$($d$)$ Which method $($Trapezoidal or Simpson's$)$ do you think is better to use? Justify your answer.

$[2]$ please use octave