Consider the integral ${\displaystyle \underset{1}{\overset{e^2}{}}}\frac{5}{x}dx$ 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?

$T(4)=($Round to six decimal places as needed.$)$