Simpson's rule is a method for numerical integration that approximates the value of a definite integral by using quadratic polynomials. It is particularly useful for functions that are difficult to integrate analytically.
5 Must Know Facts For Your Next Test
Simpson's rule uses parabolic segments to approximate the area under a curve.
The formula for Simpson's rule over an interval $[a, b]$ with $n$ subintervals (where $n$ must be even) is given by: $$\int_{a}^{b} f(x) \, dx \approx \frac{b-a}{3n} [f(a) + 4 \sum_{i=1,3,5,...}^{n-1} f(x_i) + 2 \sum_{i=2,4,6,...}^{n-2} f(x_i) + f(b)]$$
Simpson's rule requires that the number of subintervals (n) be even.
It provides more accurate results compared to the trapezoidal rule when applied to smooth functions.
The error term in Simpson's Rule is proportional to the fourth derivative of the function being integrated.