Just making sure my first expert that did this problem is around the same or the same result, please solve both problems thank you.

Using appropriate loop statement to iterate a specified n number of times, write

a Matlab script to integrate by the Simpson method $($note: n is a even number

for the Simpson$$s method$).$ The code that you are writing should be your own

code, not from some other source. To better understand how to program it$,$

you can first use an ordinary calculator to solve each step considering small n

values. Such a trial could also help you debug your code. Adopt the code to

solve the two problems given below.

$3\mathrm{.}1$ Problem #$1$

Consider the following integration as a test case for your script.

${\displaystyle \underset{0}{\overset{2}{}}}{x}^{2}dx$

Use the MatLab script that you have written to solve the above integral.

Test with different values for $n($say $n=2,n=4,n=40,n=400).$

Comment on the results that you get for different $n$ values.

$3\mathrm{.}2$ Problem #$2$

The velocity of a particle moving along a straight line for a short period of time

$0t4s$ is given as $v=60(1-e^{-t^2}).$ Determine how far the particle travels

in $t=2s.$

Use the MatLab script that you have written to solve the above integral.

Test to see if the result changes with different $n$ values $($you can choose$).$

Report your result when you use $n=50$ with the Simpson's method.