We can get a quick approximation for definite integrals when we divide a small interval [a, b] into two parts. Therefore, after dividing the interval, we get;
x0= a, x1= a + b, x2 = b

Hence, we can write the approximation as;

a∫b f(x) dx ≈ S2 = 3h/8[f(x0) + 2f(x1) + 3f(x2)]

S2 = 3h/8 [f(a) + 2f(x1)+3f(x2) + f(b)]

Where h = (b - a)/2

This is the Simpson's 3/8 rule for integration.