How do I numerically integrate using the composite trapezoidal rule in Matlab?

A problem I have to solve:

Write and submit a generic function for computing a numerical integral of a variable y using the composite trapezoidal rule. Use two input variables, x and y, where both are identically sized arrays. The variable y should represent the function you want to integrate evaluated at the points defined in x.

I am not very gifted in using Matlab syntax or numerical approximation. Can someone edit my code or help me understand how to solve this problem?

My code:

function[AreaT]=comptrap(x,y)
b=x(end)
a=x(1)
term2=0
for i=2(length(y)-1)
    term2=term2+y(i);
end
h=(b-a)/(length(x)-1)
AreaT=(h/2)*(y(1))+2*term2+y(end);

Please help, Thanks

Answer 1

[Swastik Sarkar]

Hi @Maclane Keohane,

The implementation of the composite trapezoid rule appears correct. Below is an enhanced version of the code that includes handling for edge cases and utilizes vectorization for summing terms:

function [AreaT] = comptrap(x, y)

    if length(x) ~= length(y)
        error('x and y must be vectors of the same length.');
    end

    n = length(x) - 1;

    h = (x(end) - x(1)) / n;
    
    term2 = sum(y(2:n));

    AreaT = (h / 2) * (y(1) + 2 * term2 + y(end));
end

Hope this helps.