Relating Simpson's Rule with Trapezoidal and Midpoint Rules

In this video I go further into the Simpson's Rule for approximating integrals and prove that it is in fact a weighted average of both the Trapezoidal and Midpoint Rules. As shown in my earlier videos that the Trapezoidal and Midpoint Rules have error values that are usually opposite in signs, a weighted average (and thus Simpson's Rule) is usually much more accurate than either two integration rules. In this video I go over the proof by a clever method of breaking a function into 2n sub-intervals for the Simpson's Rule while using only the even intervals in estimating the function using the Trapezoidal Rule and only the odd intervals for the Midpoint Rule approximation. This is a very interesting way of proving that it is a weighted average so make sure to watch this video!

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Related Videos:

Approximate Integration: Example 4: Simpson's Rule: https://youtu.be/7xpdZnT6IWU Approximate Integration: Simpson's Rule: Proof: https://youtu.be/aDvSpOHQoLU Approximate Integration: Midpoint Rule Error Bound: Proof: http://youtu.be/aKUFHXNeW7Y Approximate Integration: Example 1: 1/x: http://youtu.be/DTzZ1jz6OOg Approximate Integration: Accuracy and Error Bounds: http://youtu.be/WTdNktL_1Uc Approximate Integration: Trapezoidal Rule Error Bound: Proof: http://youtu.be/_mrSHIin7Mw Integration by Parts: Integration Constants: http://youtu.be/jJ-RJTNMy4s Evaluating Integrals - Midpoint vs Right Endpoint Approximations Comparison: http://youtu.be/3x3sF7P9xfY .

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