Introduction

Numerical integration using Newton formulae:

• can handle any function;
• simple;
• can handle measured data easily.

Trapezium rule for an interval from x=x_i to x_i+1:

Simpson rule for an interval from x=x_i to x_i+1:

These rules are accurate if the interval from x_i to x_i+1 is sufficiently small. To integrate over an interval that is not small, divide it into small ones, then integrate over each small interval and add the results.