Analytic and Numerical Integration (Simpsons Rule)
Simpson's Rule is a method for approximating the integral of some function over a given interval .
This is accomplished by dividing the interval into equal segments. Taking the endpoints of each sub-interval as well as their respective midpoint, a quadratic function can be determined to pass through all three points evaluated in where . Each quadratic is then integrated and evaluated over its respective interval. As , the sum of these definite integrals tends to the actual value of the original integral.