Consider the integral ${\displaystyle \underset{1}{\overset{e}{}}}\frac{5}{x}dx$ with $n=4.$

$a.$ Find the trapezoid rule approximations $to$ the integral using $n$ and $2n$ subintervals.

$b.$ Find the Simpson's rule approximation $to$ the integral using $2n$ subintervals.

$c.$ Compute the $absolute$ errors $in$ the trapezoid rule and Simpson's rule with $2n$ subintervals.

$a.$ What $is$ the trapezoid approximation with $n$ subintervals?

$T(4)=,(Roundto$ six decimal places $as$ needed.$)$