Implement all three methods $($Trapezoidal$,$ Simpson's, and Gauss Quadrature$)$ in VBA for the following integral:

$\backslash [$

$\backslash$int$\_\{0\}^\{3\}$ x$^\{4\}-2$ x$^\{3\}+$x$^\{2\}$ d x

$\backslash ]$

Use $10$ subintervals $($panels$)$ for Trapezoidal and Simpson's methods and apply $2-$point Gauss Quadrature. $[20$ marks$]$

Discussion:

$-$ Compare the results from each method and the exact value of the integral using relative error.

$-$ Which method provides the most accurate result for this specific function? Why? $($use the Excel spreadsheet part to answer$)[5$ marks$]$

Note that you will be marked on:

$-$ functionality of the code,

$-$ correct results

$-$ After reviewing the instructions,

$-$ How the results are presented

$-$ inputs that are used

$-$ Understanding the Bisection method and Newton$-$Raphson method steps

$-$ Including some form of non$-$convergence criteria or message