Time for some numerical integration. Consider the integral

$\frac{1}{2}{\displaystyle \underset{0}{\overset{2}{}}}{e}^{\frac{1}{\sqrt[\phantom{2}]{2}}sinx}dx$

$($a$)$ Write a Matlab program which uses the composite trapezoid rule to ap$-$

proximate the value of this integral for $h=\frac{1}{2}$ and $h=\frac{1}{4}.$

$($b$)$

Write a Matlab program which uses composite Simpson's rule to do the

same for the same values of $h.$ You may use another method to integrate over

the last sub$-$interval, since there are an odd number of integration nodes