Answer Happy

Question 3 (18 marks) Use SIX decimal places for all the workings. Given the definite integral in x dx. (a) Find the actual value for the definite integral. (b) Find the number of points if Composite Simpson's Rule is used to approximate the definite integral with an error of at most 3x10³. (c) Approximate the definite integral by using the Romberg algorithm to complete the following table, where R(n,m) is an integral for n=0,1,2 and m = 0,1,2. Show all your working steps and tabulate your answers as the following. 0 1 2 m R(0,0) 1 R(1,0) R(1,1) 2 R(2,0) R(2,1) R(2,2) Find the absolute error for (c).