Composite Simpson's 1/3 rule code error

I'm trying to use the composite simpsons 1/3 rule but the code is giving me an error message.

fx=1-exp(-x);
n = 5;
x = linspace(0, 4,1000);
h = (x(end) - x(1))/n;              % width of each segment
x_simp = linspace(0, 4, n+1);

for k = 1:n
    x_simp_begin(k) = x_simp(k);
    x_simp_end(k) = x_simp(k+1);
    x_simp_mid(k) = (x_simp_begin(k) + x_simp_end(k))/2;
    fx_simp_begin(k) = fx(x_simp_begin(k));
    fx_simp_end(k) = fx(x_simp_end(k));
    fx_simp_mid(k) = fx(x_simp_mid(k));
    I_simp_seg(k) = h/6*(fx_simp_begin(k) + 4*fx_simp_mid(k) + fx_simp_end(k));
end

I_simp = sum(I_simp_seg)

Error message:

Array indices must be positive integers or logical values.

Answer 1

[John D'Errico]

Tell me, what is fx?

fx is NOT a function. It is a scalar, vector, or array. Whatever x was, fx is the same thing. If it NOT a function that you can evaluate at some point. So then, when you write

I_simp_seg = 1/6*(fx(0) + 4*fx(mid) + fx(4));

what does MATLAB do? It KNOWs that fx is a variable. It tries to index the variable at position 0. What did it tell you?

Array indices must be positive integers or logical values.

You need to learn how to write a FUNCTION that can be passed arguments. You MIGHT try a function handle.

doc function_handle

A simple example for your problem here would be

fx = @(x) 1-exp(-x);

Answer 2

[Steve Areola]

clc

a=0;b=2;n=8;

h=(b-a)/n;

f=@(x) exp(2*x)*sin(3*x);

XI0= f(a) +f(b);

XI1 = 0;

XI2 = 0;

for i = 1:n-1

x = a+i*h;

if mod(i,2)==0

XI2=XI2 + f(x);

else

XI1 = XI1 + f(x);

end

end

XI=(h/3)*(XI0+2*XI2+4*XI1);

fprintf("the approximation of the integral is equal to %0.9f",XI)