Jan 11, 2020 · In the Trapezoid Rule we approximated the curve with a straight line. For Simpson’s Rule we are going to approximate the function with a quadratic and we’re going to require that the quadratic agree with three of the points from our subintervals. Below is a sketch of this using \(n = 6\). In numerical integration, we want to approximate this integral I by a sum IN A beautiful, powerful, and far-reaching way to rigorously analyze the approximation errors in the trapezoidal rule is to use Fourier analysis, which relies on an amazing fact: any "reasonable" function can be expressed as an...