LegRuleCalculator

How to Use the LegRuleCalculator

1. Enter the function you want to integrate in the "Function (f(x))" field. For example, enter "x^2 + 2*x + 1" for the quadratic function.
2. Specify the lower limit of integration in the "Lower Limit (a)" field.
3. Specify the upper limit of integration in the "Upper Limit (b)" field.
4. Enter the number of intervals (n) in the "Number of Intervals (n)" field. A higher number of intervals will give a more accurate result.
5. Click the "Calculate" button to perform the integration.
6. The result will be displayed in the "Result" field.

Working Principle

The LegRuleCalculator uses Legendre's rule for numerical integration. Legendre's rule is a method for approximating the definite integral of a function. It works by dividing the interval of integration into n equal subintervals and applying a weighted sum of the function values at specific points within each subinterval.

The formula for Legendre's rule is:

∫_a^b f(x) dx ≈ (h/3) * [f(x₀) + 4*f(x₁) + 2*f(x₂) + 4*f(x₃) + ... + 2*f(x_n-2) + 4*f(x_n-1) + f(x_n)]

where h = (b - a) / n is the width of each subinterval, and x_i are the points within each subinterval.