# Numerical integration rules

This is a demonstration of rules for numerical integration used to approximate $$\int_{-1}^3 \frac{2}{1 + 4x^2} \ dx$$.

Clicking the "Double intervals" button will double the current number of intervals and display the ratio of successive errors.

Note: The exact value of this integral is $$\tan^{-1}(4) + \tan^{-1}(2)$$, which is, to eight decimal places, 2.43296638.

Select method:
Right-hand rule
Left-hand rule
Midpoint rule
Trapezoidal rule
Simpson's rule

Number of intervals: