puolisuunnikassääntöjä

Puolisuunnikassääntöjä, known in English as the trapezoidal rule, is a numerical method for approximating the definite integral of a function. It is based on approximating the region under the curve of a function as a series of trapezoids rather than rectangles, as is done in the simpler rectangular rule.

The basic idea of the trapezoidal rule is to divide the interval of integration [a, b] into n subintervals of equal width, denoted by h = (b - a) / n. For each subinterval, the function's curve is approximated by a straight line connecting the function's values at the endpoints of the subinterval. This forms a trapezoid. The area of each trapezoid is then calculated and summed up to approximate the total area under the curve.

The formula for the trapezoidal rule is given by:

Integral from a to b of f(x) dx ≈ (h/2) * [f(x₀) + 2f(x₁) + 2f(x₂) + ... + 2f(x<0xE2><0x82><0x99>₋₁) + f(x<0xE2><0x82><0x99>)]

where xᵢ = a + i*h for i = 0, 1, ..., n.

The accuracy of the approximation generally increases as the number of subintervals (n) increases, meaning h decreases. The trapezoidal rule is a foundational concept in numerical integration and is often taught as an intermediate step between simpler methods like the midpoint rule and more advanced techniques like Simpson's rule.