Suorakulmiomenetelmässä

Suorakulmiomenetelmä is a numerical integration technique used to approximate the definite integral of a function. It falls under the category of quadrature methods, which aim to find the numerical value of an integral. The core idea of the suorakulmiomenetelmä is to divide the area under the curve of the function into a series of rectangles and then sum the areas of these rectangles.

There are three main variations of the suorakulmiomenetelmä: the left-hand rule, the right-hand rule, and the midpoint rule. In the left-hand rule, the height of each rectangle is determined by the function's value at the left endpoint of the interval. Conversely, the right-hand rule uses the right endpoint. The midpoint rule, often considered more accurate, uses the function's value at the midpoint of each interval to define the rectangle's height.

To apply the suorakulmiomenetelmä, the interval of integration is first divided into a specified number of subintervals of equal width. The width of each subinterval is calculated by dividing the total length of the integration interval by the number of subintervals. For each subinterval, a representative function value is chosen (left endpoint, right endpoint, or midpoint) to determine the height of the rectangle. The area of each rectangle is then calculated by multiplying its height by the width of the subinterval. Finally, these individual rectangle areas are summed to obtain the approximation of the definite integral. As the number of rectangles increases, the approximation generally becomes more accurate, approaching the true value of the integral.