$22\mathrm{.}10$ Develop a user$-$friendly computer program for the multiplesegment $22\mathrm{.}10$ Develop a user$-$friendly computer program for the multiple$-$

segment $($a$)$ trapezoidal and $($b$)$ Simpson's $\frac{1}{3}$ rule based on

Fig. $22\mathrm{.}1.$ Test it by integrating

${\displaystyle \underset{0}{\overset{1}{}}}{x}^{0\mathrm{.}1}(1\mathrm{.}2-x)(1-e^{20(x-1)})dx$

Use the true value of $0\mathrm{.}602298$ to compute ${}_t$ for $n=4.$

$($a$)$ trapezoidal and $($b$)$ Simpson$$s $1$y$3$ rule based on

Fig. $22\mathrm{.}1.$ Test it by integrating

#$1$

$0$

x$0\mathrm{.}1(1\mathrm{.}22$ x$)(12$ e$20($x$21))$ dx