Suorakulmiosääntö

The suorakulmiosääntö, or rectangular rule, is a numerical integration method used to approximate the definite integral of a function. It is one of the simplest methods for numerical integration. The basic idea is to divide the area under the curve of the function into a series of rectangles and then sum the areas of these rectangles.

The interval of integration is divided into a number of equal subintervals. On each subinterval, a rectangle is constructed whose width is the length of the subinterval and whose height is determined by the function's value at a specific point within that subinterval. There are three common variants of the rectangular rule depending on where the height is evaluated: the left rectangular rule uses the left endpoint of the subinterval, the right rectangular rule uses the right endpoint, and the midpoint rule uses the midpoint of the subinterval.

The accuracy of the approximation generally increases with the number of subintervals used. As the number of subintervals approaches infinity, the approximation converges to the exact value of the definite integral. While simple to understand and implement, the rectangular rule is often less accurate than other numerical integration methods, such as the trapezoidal rule or Simpson's rule, for the same number of function evaluations. However, its simplicity makes it a useful introductory method for understanding numerical integration concepts.