Midpoint Rule

Approximating areas under curved boundaries is a common problem in applied mathematics, particularly when an exact calculation is difficult or impractical. One effective numerical method for this purpose is the Midpoint Rule, which provides an estimate of the area under a curve by using rectangular approximations over a specified interval.

The Midpoint rule helps estimate the area under a curve by dividing the interval into equal subintervals.

The midpoint of each subinterval is calculated as the average of its two endpoints. The function’s value at these midpoints gives the height of rectangles drawn over them. This approach often gives a more accurate estimate than methods...