Rectangle method

The midpoint rule (also rectangular rule or tangent trapezoidal rule ) is a numerical method for the approximate calculation of integrals ( Numerical quadrature ). It takes on the midpoint of the interval [a, b ] and multiplied the function value at this point with the interval width (ba ) to get the integral:

If you turn the picture above the midpoint rule, the horizontal line at the point counterclockwise, we obtain the tangent for the point. This results in the image below the tangent trapezoid rule. Since the trapezoidal thus obtained has the same area as the rectangular, thus, the midpoint rule, and the tangent trapezoidal rule are various geometric interpretations of the same quadrature formula.

Divided into n sub-intervals, wherein the composite control center or the composite tangent trapezoidal rule then the interval [b a]. Then, it executes the midpoint rule for each of the sub-intervals and sums the surfaces.

Example

It is a function in the interval [ 2, 6 ] to integrate. For this purpose, the calculation of the integral would be necessary. The general solution is:

It is always advisable

When using the composite midpoint rule with four subintervals gives the following to: