Integrate the following function numerically using trapezoid rule and Simpson's $\frac{1}{3}$ rule.

$I={\displaystyle \underset{a}{\overset{b}{}}}{x}^3{e}^{x}dx$

Requirements

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

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 $\frac{1}{3}$ 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: #$.$####

Function Program

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

b$.$ output will be the area

Example