suorakulmiomenetelmä

The suorakulmiomenetelmä, also known as the rectangle method or rectangular approximation, is a technique used in calculus to approximate the area under a curve. It is a fundamental concept that leads to the development of definite integration. The method involves dividing the area beneath a given function's graph, between two points on the x-axis, into a series of vertical rectangles. The width of each rectangle is determined by dividing the interval on the x-axis into smaller, equal subintervals. The height of each rectangle is then determined by the function's value at a specific point within that subinterval. Common choices for this point include the left endpoint, the right endpoint, or the midpoint of the subinterval.

Once the rectangles are constructed, their areas are calculated individually. The sum of the areas of all these rectangles provides an approximation of the total area under the curve. As the number of rectangles increases, meaning the width of each rectangle decreases, the approximation becomes more accurate. In the limit, as the number of rectangles approaches infinity, the sum of the areas of these rectangles converges to the exact area under the curve, which is the definition of the definite integral. The suorakulmiomenetelmä serves as an intuitive way to understand how integration works by breaking down a continuous area into discrete, manageable parts.