Q$.4$ a$)$ Use the Composite Simpson's rule with the indicated value of $n$ to approximate the following integral: $(15$ pts $)$

${\displaystyle \underset{-2}{\overset{2}{}}}{x}^3{e}^{x}dx,n=4$

Formula:

${\displaystyle \underset{a}{\overset{b}{}}}f(x)=\frac{h}{3}[f(a)2{\displaystyle \underset{j=1}{\overset{(\frac{n}{2})-1}{}}}f(x_{2j})4{\displaystyle \underset{j=1}{\overset{\frac{n}{2}}{}}}f(x_{2j-1})f(b)]-\frac{b-a}{180}{h}^4{f}^{(4)}()$

b$)$ Apply the Gauss$-$Seidel iterative technique to find approximate solutions to:

$20x_1{x}_2-2x_3=17$

$3x_{1}20x_2-x_3=-18$

$20x_1-3x_{2}20x_3=25$

starting with $x=(0,0,0{)}^t.$

$(15$ pts$)$