Problem:

Integrate the following function numerically using trapezoid rule and Simpson$$s $1/3$ rule.

$=3$

$$

$$

Requirements

$1.$ For each method, you will need a driver program and a function program.

$2.$ Driver program will be used to:

a$.$ define f$($x$)$ as a function handle

b$.$ enter the values for a$,$ b$,$ and n $($i$.$e$.$ the range and the number of subdivisions

between x $=$ a and x $=$ b$).$ These numbers are to be entered using the input

command.

i$.$ You can assume that n is greater than $1.$ To use the Simpson$$s $1/3$ rules, n

should be an even number $($n is the number of subdivisions$).$

c$.$ call the function program to determine the area.

d$.$ print out the results of the integral. Output should be as follows:

The value of the integral from a $=$ # to b $=$ #

using # equally spaced divisions is: #$.$#####

$3.$ Function Program

a$.$ inputs to function program are: a$,$b$,$ n$,$ and your function handle

b$.$ output will be the area