Problem 3 Sophomore's Dream Consider the true value of the following definite integral: 1 x* dx = 0.7834305107 (up to 10 significant digits). Submit a MATLAB script to numerically compute the above integral using (a) the midpoint method with x-axis partition (0,1/2], (1/2, 1]; (b) the trapezoid method with the same x-axis partition as in part (a); and (c) the three point Simp- son's method. Your MATLAB script should look like the following (fill in the right hand sides of I midpoint etc.), and should print the relative errors up to 10 significant digits in (a), (b), (c). close all; clear; clc; format long f = Q(x) x. ^x; I_true = 0.7834305107; I_midpoint = ; I_trapezoid = ; I_simpson = ; rel_err_midpoint = chop(abs ((I_true - I_midpoint)/I_true) ,10) rel_err_trapezoid = chop (abs((I_true - I_trapezoid)/I_true) ,10) rel_err_simpson = chop(abs((I_true - I_simpson)/I_true), 10)