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:

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