Objective: pleaseeeeeeeeeeeeeeeeeeeeeeeeeeee sole this as soon as possibleeeeeeeeeeeeeee

The objective of this assignment is for the learners to demonstrate that they can

Conduct basic scientific research.

Carry out work$/$assignments responsibly.

Interpret the results of the numerical methods.

CILOs:

This assignment measures CILOs $4$ and $7.$

Task:

Research the Romberg method to approximate the integral of a given function. The research should cover the

following points:

A brief introduction of the method $($covers who created it$,$ when? Why, and how to apply it$).$

The advantages and disadvantages of the method compared to the method we studied

$($Trapezoidal and Simpson's$).$

Let ${\displaystyle \underset{0}{\overset{1}{}}}x{e}^{x}dx$ and $h=0$

a$)$ Use Simpson's method to approximate the integral.

b$)$ Apply Romberg integration to approximate the integral $($Stop at $R_{33})$

c$)$ Which method gives a better approximation? Is this what you expected? Justify your answer.$[2]$

List of references $($at least $2)$ written in Harvard referencing style. Note that Wikipedia is not

acceptable as a reliable academic resource.

Instructions:

Name the assignment file as ID$\_$First$\_$Name$\_$Research $($e$.$g$.,211122234\_$Thuraya$\_$Research$).$

Number the pages.

The cover page must include the following:

a$)$ Your name, Student ID$,$ and Assignment title.

b$)$ The declaration: Hereby, I declare that I did the assignment by myself

Do the calculations using $4$ decimal places.

Upload your assignment on Blackboard. You have three attempts to submit the assignment. In

addition, submit a hard copy.

Avoid plagiarism by writing the references and resources you used, such as books or websites, in

Harvard referencing style. Note that Wikipedia is not acceptable as a reliable academic resource.

Note that the Safe Assign is enabled to check for originality.

The total mark is distributed as $13$ points for the written paper and $3$ for the oral discussions.

This is a summative assessment; it will be included in your final grade as $8\%.$