Question

PLEASE PLEASE,ONLY ANSWER THIS QUESTION IF YOU COULD GIVE ME THE MATLAB CODE.THANK YOU.

Use Simpson's 3/8 rule with n segments to approximate the integral of the following function on interval [3, 10] 2.(x-3) f(x) = 1.385 · sin( 243-2) The exact value of the integral is Texact = 6.8648 Fill in the blank spaces in the following table. Round up your answers to 4 decimals. Relative error &, is defined as | I - Iexact * 100% Iexact n, segments I, integral E = € (%) 13 6

Answer 1

MATLAB Script:

close all
clear
clc

syms x
a = 3; b = 10; % Integration interval
f = 1.385 * sin(2*(x - 3)/7); % Function to be integrated
I_Exact = 6.8648;

N = [3, 6]; % Number of sub-intervals
Rel_Err_Simps = zeros(1, length(N));
fprintf('%-10s%-20s%-30s\n', 'N', 'I (Simps.)', 'Rel. Err. (Simps.) %')
for i = 1:length(N)
n = N(i);
I_Simps = CompositeSimpson38Rule(f, a, b, n);
Rel_Err_Simps(i) = abs((I_Simps - I_Exact)/I_Exact) * 100;
fprintf('%-10d%-20.4f%-30.4f\n', n, I_Simps, Rel_Err_Simps(i))
end

function I = CompositeSimpson38Rule(f, a, b, n)
h = (b - a)/n;
x_vals = a:h:b; % Nodes
I = (3*h/8) * ( subs(f, x_vals(1)) + ...
3*sum(subs(f, x_vals(2:3:end-1))) + ...
3*sum(subs(f, x_vals(3:3:end-1))) + ...
2*sum(subs(f, x_vals(4:3:end-1))) + ...
subs(f, x_vals(end)) ); % Composite Simpson's 3/8 Rule
end

Output:

Command Window N I (Simps.) 3 6.8837 6 6.8659 fx >> | Rel. Err. (Simps.) % 0.2756 0.0154