Integrointiraja
Integrointiraja, also known as the *integral triangle* or *integral triangle rule*, is a mathematical concept used in numerical integration to approximate the value of a definite integral. It is a specific case of the composite trapezoidal rule, where the interval of integration is divided into an even number of subintervals, and the trapezoidal rule is applied in pairs of adjacent subintervals. This method is particularly useful for improving the accuracy of numerical approximations when the integrand has certain symmetry properties.
The integral triangle rule is derived from the trapezoidal rule but refines it by combining trapezoids in
(Δx/2) * [f(a) + 2Σf(x_i) + f(b)] + (Δx/2) * [f(a + Δx) + f(a + 3Δx) + ... + f(b − Δx)]
This simplifies to a weighted sum of function values at evenly spaced points, where the endpoints are
Integrointiraja is often compared to other numerical integration techniques, such as Simpson’s rule, which also improves