I need help with this matlab problem. Consider again the error function integral from PA$6$:

erf$(x)=\frac{2}{\sqrt[\phantom{2}]{}}{\displaystyle \underset{0}{\overset{x}{}}}{e}^{-t^2}dt$

For this problem you'll use the following numerical integration approaches to evaluate this integral and generate values for a table similar to what you worked with in PA$6.$

Composite trapezoid rule $($MATLAB trapz and$/$or cumtrapz functions$).$

Three point Gauss$-$Legendre quadrature.

MATLAB's built$-$in integral function $($Adaptive Gauss$-$Kronrod Quadrature$).$

Write a function that receives the following single input:

A column vector of one or more $x$ values at which erf$(x)$ is to be computed.$|$

Your function should return the following outputs $($in order, column vectors when input $x$ is a vector$)$:

The estimate$($s$)$ for erf $(x)$ calculated using composite trapezoid rule between $0$ and each of the elements in $x.$ Evaluate the integrand at $0$ and at the input $x-$values to compute $y-$values for the trapezoid rule.

The estimate$($s$)$ of erf $(x)$ calculated using three$-$point Gauss$-$Legendre quadrature. Work by hand to develop the shifted integrand $($in terms of $x_d)$ and use the appropriate constants and function evaluations.

The estimate$($s$)$ of erf$(x)$ calculated using MATLAB's built$-$in integral function.

Note: The first three test cases use a scalar input for $x$ and check each of the methods separately. Code to call your function $($e$)$