Romberg Integration

Consider the integral given in problem $1.$

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

Show all the steps in your code $($NO LOOP!!!!!!!$)$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:

j k$=1$ k$=2$ k$=3$ k$=4$

$--------------------------------------------------$

$1$ xxxxx$.$xxxxx xxxxx$.$xxxxx xxxxx$.$xxxxx xxxxx$.$xxxxxxxxxx

$2$ xxxxx$.$xxxxx xxxxx$.$xxxxx xxxxx$.$xxxxx

$3$ xxxxx$.$xxxxx xxxxx$.$xxxxx

$4$ xxxxx$.$xxxxx

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.