Numerical Integration: Simpson's 1/3 Rule | Theory and Python & Numpy Implementation
Simpson's Rule is a numerical integration method used to approximate the definite integral of a function over a specified interval. It is named after the 19th-century mathematician Thomas Simpson. This method is particularly useful when you have tabulated data or when you're dealing with a function that doesn't have a straightforward elementary antiderivative.
The main idea behind Simpson's Rule is to approximate the area under a curve by dividing the interval into a series of smaller subintervals and then using quadratic (second-degree) polynomials to approximate the curve within each of these subintervals. The resulting approximations are then summed up to estimate the integral.
Simpson's Rule offers a balance between computational simplicity and accuracy, making it a valuable tool for approximating definite integrals, especially when more sophisticated integration techniques are impractical.
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animation courtesy: https://en.wikipedia.org/wiki/Simpson...
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