1. (45 points) Evaluate by hand the definite integrals below. Subsequently, approx imate them by using the composite Trapezoidal ruletrap (h) for N-2, 4, 8, 16, 32 and 64, where h = (b-a)/N (a) (15 points) I(3x +1) dr (b) (15 points) If-xe dax (c) (15 points) I, To do so, write a MATLAB function (or in any other programming language) stored (cos (x) + 1) dr as trap.m whose first line should read function [y ] = trap ( f, a, b, N ) Include a copy of your code. For each of the cases above make a table with columns: column 1: N column 2: h . column 3: 1trap(h) (this is the approximation, i.e., the output y ) Column 4: |error! (this Is the absolute error) . column 5: errorl/h2 Are the numbers in the last column converging, and if so, what does this mean? Specifically, comment on the behavior of the error for (a) and (b). If your code is correct, you will notice that for (c) the last column is not converging, and that the approximation is very accurate. Can you explain briefly why