Create a function using matlab to compute integral numerically using Simpson$$s $3/8$ Rule, that complete the integration with either Simpson$$s $1/3$ Rule or Trapezoidal Rule $($whichever may be possible$)$:

function integral $=$ mysimpsons$38($x$,$ f$)$

$\%$ Integrates numerically using Simpson's $3/8$ Rule and completes the integration with

$\%$ either Simpson$$s $1/3$ or Trapezoidal Rule as applicable.

$\%$ Input:

$\%=====$

$\%$ x $=$ vector of independent variable values

$\%$ f $=$ vector of corresponding function values

$\%$ Output:

$\%=======$

$\%$ integral $=$ numerically computed integral value

Integrate the following using both MATLAB$$s integral$()$ and mysimpsons$38()$ and discuss your comparison:

limits of integration from $2$ to $1($x $+1/$x$)^2$ dx