Fitness

Why Simpson's Rule can achieve better accuracy, then the trapezoids?

Can anyone explain why Simpson rule can achieve better accuracy and trapezoidal rule for refining a curved area. A big thank you.

Rule Simpson uses a quadratic approximation, while the trapezoidal rule uses a linear approximation of the function on each interval. A quadratic approximation has a degree of freedom additional meaning it can more closely approximate the original curve.

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