LegRuleCalculator

How to Use the Calculator

1. Enter the function you want to integrate in the "Function to Integrate" field. Use standard mathematical expressions (e.g., x^2 + 2*x + 1).
2. Set the lower and upper limits of the integration interval.
3. Choose the number of points for the quadrature. Currently, only 3 points (Gauss-Legendre quadrature) are supported.
4. Click the "Calculate" button to compute the integral.
5. The result will be displayed in the "Result" section.

Working Principle

The Legendre-Gauss quadrature method approximates the integral of a function by evaluating the function at specific points (nodes) within the interval and weighting these evaluations. The formula used is:

∫_a^b f(x) dx ≈ Σ_i=1ⁿ w_i * f(x_i)

Where:

• w_i are the weights for the nodes.
• x_i are the nodes (points) where the function is evaluated.
• n is the number of points used for the quadrature.

This method provides accurate results for many well-behaved functions and is particularly useful for high-dimensional integrals.