(Solved): 3. (Numerical Integration: Composite Rectangle Rule). (i) Use the Composite Rectangle Rule with n ...

3. (Numerical Integration: Composite Rectangle Rule). (i) Use the Composite Rectangle Rule with n = 20 to find an approximation I* of the integral 0.5 I = In (53.4 + sin² x) da 132 Show your work by filling in the third column of the following table of selected values of the integrand: k xk ?? 0 5 0 0.125 0.25 10 15 0.375 19 0.475 (you can create-for your own use-a full standard table the method requires in the process of the solution, but please provide just the selected values in your work, as instructed). (ii) Form a suitable command/query to execute at the Wolfram Alpha website to find the 12-digit representation J of I, and then find the relative error and the number of significant digits in approximation of J by I*. All calculations are to be carried out in the FPA9.