calculate the error of an integral from a 2 column data set using repeat simpsons rule in matlab

To calculate the error of an integral from a 2 column data set using repeated Simpson's rule in MATLAB, you can follow the steps given below:

1. Load the data set using the load command in MATLAB:

main.m
data = load('data_set.txt');
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2. Define the function to be integrated using anonymous functions in MATLAB:

main.m
f = @(x) x.^2 + 2.*x - 1;
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3. Define the limits of integration using the min and max commands in MATLAB:

main.m
a = min(data(:,1));
b = max(data(:,1));
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4. Determine the number of subintervals needed for the repeated Simpson's rule:

main.m
n = length(data(:,1))-1;
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5. Calculate the step size:

main.m
h = (b-a)/n;
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6. Use a loop to calculate the integral using the repeated Simpson's rule formula:

main.m
sum1 = 0;
for i = 1:2:n-1
    sum1 = sum1 + f(data(i,1)) + 4*f(data(i+1,1)) + f(data(i+2,1));
end
integral = (h/3)*sum1;
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7. Calculate the error using the error formula for Simpson's rule:

main.m
error = ((b-a)/12)*((h).^4)*max(abs(diff(diff(f(data(:,1))))));
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8. Display the calculated integral and error using the disp command in MATLAB:

main.m
disp(['Integral: ', num2str(integral)]);
disp(['Error: ', num2str(error)]);
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Note that in the above code, it is assumed that the 2 column data set is stored in a text file named "data_set.txt" in the current working directory. If this is not the case, you will need to modify the path in the load command accordingly.