Estimating Area with Simpson’s Rule

Simpson’s Rule is a numerical integration method for estimating the value of a definite integral. It is useful when an exact antiderivative is hard or impossible to find. The method works by fitting a unique parabola through three equally spaced points on a curve and then integrating that quadratic over the interval.

Surveyors often calculate the area of uneven land strips, like the region between a straight road and a curved riverbank.

Since the river’s curved boundary usually does not have a simple mathematical equation, Simpson’s Rule is used.

Simpson’s rule, based on a numerical integration method, estimates the area using only a few sampled ...