function main

    format compact
    format long
    x0 = 1
    x2 = 2
    f = @(x) log(x)
    approxI = mysimpson(f,x0,x2)
    exact_I = AntiderivativeOfLog(x2) - AntiderivativeOfLog(x0)
    error = approxI - exact_I
    relativeError = error/exact_I

end


function I=mysimpson(f,x0,x2)
   h = (x2 - x0)/2;
   x1 = x0 + h;
   I = h/3 * ( f(x0) + 4*f(x1) + f(x2) );
end


function y=AntiderivativeOfLog(x)
   y = x*log(x) - x;
end