Which computing technique is useful for finding the area of irregular boundaries?

The Simpson's One-Third Rule is a numerical method that is particularly effective for estimating the area under a curve, which can be valuable when dealing with irregular boundaries. This technique breaks the area into smaller segments and fits parabolic arcs instead of straight-line approximations, making it more accurate for curves. The rule requires that the number of intervals be even, allowing it to utilize the properties of quadratic polynomials to provide good approximations even in cases where the geometry is complex.

This method is especially useful in surveying when calculating areas that do not conform to standard geometric shapes. When applied correctly, Simpson's One-Third Rule gives results that are generally closer to the true area than simpler techniques, especially for curves that would be misrepresented by linear methods.

Other methods like the Trapezoidal Rule are less precise for irregular shapes since they approximate areas using trapezoids, which may not capture the curvature effectively. The Monte Carlo Method is more suited for probabilistic simulations rather than direct area calculations, and Newman’s Method, while useful in some contexts, does not specifically address the challenge of calculating areas of irregular shapes in the same way that the Simpson's One-Third Rule does.