Evaluate the following integral with detalled solations:

$I={\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}(8+4cosx)dx$

a$)$ Analytically

b$)$ Single application of the trapezoidal rule.

c$)$ Multiple$-$application trapezoidal rule, with $n=4.$

d$)$ Sinde application of Simpson's $\frac{3}{8}$ rule

e$)$ For each of the numerical estimates $($b$-$d$)$ through $($e$),$ determine the

percent relative error based on $($a$).$USE MATLAB ONLY