Anonymous Functions and Function Handles. Remember to write text that ex$-$ plains your solution and introduces all code and output that you include. This text should come first, before all code and output.

First write a function simp$($f$,$ a$,$ b$,$ n$)$ which uses Simpson$$s rule

Zbhh i

f$($x$)$dx$3$ f$($x$0)+4$f$($x$1)+2$f$($x$2)+4$f$($x$3)++2$f$($xn$2)+4$f$($xn$1)+$f$($xn$),$ a

where h $=$ b$$a denotes the numerical step size for a given even integer n$,$ to approximate the n

definite integral of f$($x$)$ over the interval $[$a$,$b$].$ The implementation of the function will be very similar to that of trap.m we saw in the tutorial. Next, write a script file in which which you will define the functions

f$($x$)=$ sin$($x$)$ x in $[0,\backslash$pi $2]$ g$($x$)=$ ecos$($x$)$ x in $[0,\backslash$pi $]$

as anonymous functions and then use simp to compute the definite integral of each function over the given interval. Use n $=4,8,16,32,...,512$ and print a table as follows:

n I$($f$)$ I$($g$)$

$------------------------------$

$41\mathrm{.}09734946$

$81\mathrm{.}11043794$

$161\mathrm{.}11503637$

$321\mathrm{.}11665656$

$.$

$..$

$3\mathrm{.}97173128$

$3\mathrm{.}97746305$

$3\mathrm{.}97746326$

$3\mathrm{.}97746326$

You should note that the formula for Simpson$$s rule has a similar pattern to Homework $2$ Problem $3.$ Consider incorporating your solution from there into this problem.