Question

Complete the following problems in Matlab environment. Copy your com mand and final answer from MATLAB command window and paste them in a word document. Submit a single word document file for the entire HW Problems: Code your own MATLAB program to find the approximate value of the integral J e dr with Trapezoidal rule for N 20, .e., 2 (formula 4.21 on Page 201 YS). Also give the relative error of t2o with de-1. (Hint: For-end loops or Elementwise operations)

Answer 1

Problem:

f = @(x) exp(x);% Function to integrate

N = 20;% Number of trapezoids
a = 0;% Lower limit
b = 2;% Upper limit

%% Trapezoidal Rule
h = abs((b - a)/N);
sum = 0;
for i = 1:(N-1)
    x = a + i * h;
    sum = sum + f(x);
end
approxValue = (h/2) * (f(a) + 2 * sum + f(b));

trueValue = exp(2) - 1;
relativeError = (approxValue - trueValue)/trueValue;

fprintf('Approximate value = %f\n', approxValue);
fprintf('True value = %f\n', trueValue);
fprintf('Relative error = %f\n', relativeError);

OUTPUT:

Editor -CAUsers1 Shubhamlpractice.m practice.m ×1+ f = @ (x) exp(x);% Function to integrate N = 20;% Number of trapezoids a = 0;% Lower limit b = 2;% Upper limit %% Trapezoidal Rule h abs ( (b - a)/N); 0; sum 10 for i I: (N-1) 12 sum + f (x) ; sum end Command Window >>practice Approximate value 6.394379 True value 6.389056 Relative error = 0.000833 >y