mittpunktsmetod

The midpoint method, also known as the trapezoidal rule with one interval, is a simple numerical integration technique used to approximate the definite integral of a function. It works by approximating the area under the curve of the function over a given interval using a single rectangle. The height of this rectangle is determined by the value of the function at the midpoint of the interval.

To apply the midpoint method for an integral from 'a' to 'b' of a function f(x), the interval [a, b] is divided into subintervals. However, in its simplest form, only one subinterval is used. The midpoint of this interval is calculated as m = (a + b) / 2. The width of the interval is then b - a. The approximate integral is then given by the formula (b - a) * f(m).

The accuracy of the midpoint method depends on the function being integrated and the width of the interval. For functions that are relatively linear over the interval, the midpoint method can provide a reasonably good approximation. However, for functions with significant curvature, the approximation may be less accurate compared to more sophisticated numerical integration methods such as Simpson's rule or the trapezoidal rule with multiple subintervals. Despite its simplicity, the midpoint method is often used as a foundational concept in numerical analysis and can be extended by dividing the interval into multiple subintervals to improve accuracy.