below is the (hopefully familiar) formula for the composite trapezoidal rule: image.png briefly explain why we multiply the summation term by 2 (circled in the above equation). in matlab

In the composite trapezoidal rule formula, the summation term is multiplied by 2 to account for the fact that the function values at the interior points are counted only once in the formula, whereas the endpoints are counted twice.

In MATLAB, the composite trapezoidal rule can be implemented as follows:

main.m
function result = composite_trapezoidal_rule(f, a, b, n)
    h = (b - a) / n;  % interval width
    
    % calculate the sum of function values at interior points
    sum = 0;
    for i = 1:(n-1)
        x = a + i * h;
        sum = sum + f(x);
    end
    
    % apply the composite trapezoidal rule formula
    result = h * (f(a) + 2 * sum + f(b)) / 2;
end
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Where:

• f is the function handle representing the integrand
• a and b are the lower and upper bounds of integration
• n is the number of intervals (subintervals) used for the approximation

Note that in this implementation, the formula is applied to each subinterval separately, and then the results are summed up to obtain the final approximation.