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Simpson's Rule

Use problems 8 and 9 on p. 348 as an outline to write a clear explanation why Simpson's rule is a good way to approximate definite integrals over a finite interval.

The questions are attached, I need help explaining each step of the problem, with a few different proofs of how this actually works.

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This solution is comprised of a detailed explanation to write a clear explanation why Simpson's rule is a good way to approximate definite integrals over a finite interval.

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