Answer in MATLAB

Romberg Integration

Consider the integral given in problem $1.$

a$)$ Use the Romberg integration technique to calculate the integral with an error of $O(h^8).$

Show all the steps in your code $($no loop$).$ You can use the trap function from the

textbook but not the romberg function. Print the results in a table like the one below

using fprintf.

b$)$ Use the romberg function from the textbook with default relative error tolerance and

maximum iterations to verify your answer. Use a single fprintf statement to print the

result with $10$ digits after the decimal point as well as the number of iterations it took.