Problem$3-$In communication theory, error function is commonly used : erf$(1\mathrm{.}5)=\frac{2}{\sqrt[\phantom{2}]{}}{\displaystyle \underset{0}{\overset{1\mathrm{.}5}{}}}{e}^{-t^2}dt.$ There is no closed form solution to this integral. Hence numerical integration is employed. First determine true value from MATLAB's built$-$in function erf. Then evaluate this integral;

a$.$ Romberg integration $)=(0\mathrm{.}5\%$

b$.$ Two$-$point Gauss Legendre formula

c$.$ Three$-$point Gauss Legendre formula

d$.$ Calculate percent relative error for each case from a to c$.$