m.matlab

function I = simp(f, a, b, n)
I = 0;
dx = (b-a) / n;
for i = 1:2:n
    xi = a + (i - 1) * dx;
    xi_1 = a + (i * dx);
    xi_2 = a + (i + 1) * dx;
    
    I = I + (1/3) * (f(xi) + 4 * f(xi_1) + f(xi_2)) * dx;
end

function I = trap(f, a, b, n)
I = 0;
dx = (b-a) / n;
for i = 1:n
    xi = a + (i-1) * dx;
    xi_1 = a + i * dx;
    
    I = I + (1/2) * (f(xi) + f(xi_1)) * dx;
end

function I = simp_data(f, a, b)
I = 0;
n = length(f);
dx = (b-a) / n;
for i = 1:2:n
  I = I + (1/3) * (f(i) + 4*f(i+1) + f(i+2)) * dx;
end

function I = lhr(f, a, b, n)
I = 0;
dx = (b-a) / n;
for i = 1:n
    xi = a + (i-1) * dx;
    I = I + f(xi) * dx;
end