See my Matlab code below. This deals with integral approximation using left rect
ID: 3422548 • Letter: S
Question
See my Matlab code below. This deals with integral approximation using left rectangle, right rectangle, trapezoid, and Simpson's approximations. The goal is to plot each approximation (R,L, T, and S) against each n value. But I'm having trouble making n, R, L, T, and S vectors.
ln = input('Enter the lower bound of n (must be an even number) ');
if mod(ln,2) == 0; %number is even
ln = ln;
else %number is odd
fprintf('Error: Input must be an even number ')
return
end
% Assures that upper bound of n is even
un = input('Enter the upper bound of n (must be an even number) ');
if mod(un,2) == 0;%number is even
un = un;
else %number is odd
fprintf('Error: Input must be an even number ')
return
end
for n = ln:2:un;
x = linspace(-4,4,n+1);
h = -8./n; % h = delta x; (b-a)/n = (-4-4)/n = -8/n
f = (2.*x +1/3).*cos(x.^2 + x/3);
% Create weight functions
wL = ones(1,n+1); %one row, n+1 columns
wL(n+1) = 0; %left sum doesn't use right endpoint
wR = ones(1,n+1);
wR(1) = 0; %right sum doesn't use left endpoint
wT = ones(1,n+1);
wT(2:n) = 2;
wS = ones(1,n+1);
wS(2:2:n) = 4;
wS(3:2:n-1) = 2;
% Compute the left and right rectangle approximation
L = 0;
R = 0;
for i = 0:n
L = L + f(i+1)*wL(i+1);
R = R + f(i+1)*wR(i+1);
end
L = h*L;
R = h*R;
% Compute the trapezoid approximation
T = 0;
for i = 0:n
T = T + f(i+1)*wT(i+1);
end
T = (h/2)*T;
% Compute the Simpson's approximation
S = 0;
for i = 0:n
S = S + f(i+1)*wS(i+1);
end
S = (h/3)*S;
end
Explanation / Answer
See my Matlab code below. This deals with integral approximation using left rect