The error function erf$(2)$ is defined by $2$ erf$($x$)=$ False" $-$t$^2$ dt$.$ a$.$ Use the Gaussian quadrature with n $=2,$ n $=3,$ and n $=4$ to approximate erf$(0\mathrm{.}5)($By hand and Python$/$Matlab code.$]$ b$.$ Use the composite midpoint rule, the composite trapezoidal rule, the composite Simpson's rule $($with n $=128,$ which means the subinterval length $=($b $-$ a$)/$n$)$ to approximate erf$(0\mathrm{.}5).[$By Matlab code$]$