Hardy's Rule

Let the values of a function $f(x)$ be tabulated at intervals equally spaced by $h$ at $x_1$, $x_2$, ..., $x_7$ and let $f_n=f(x_n)$. Then Hardy's rule gives the approximation to the integral of $f(x)$ as

$$\int_{x_1}^{x_7} f(x)\,dx = {\textstyle{1\over 100}}h(28f_1+162f_2+220f_4+162f_6+28f_7).$$

See also Bode's Rule, Durand's Rule, Newton-Cotes Formulas, Simpson's 3/8 Rule, Simpson's Rule, Trapezoidal Rule, Weddle's Rule