Derive the Simpson rule with f(x) = ax^2 + bx + c going through points xi−1, xi, and xi+1. Determine a, b, and c from the three equations given at the three data points first and then carry out the integration over the two slices with the quadratic curve being the integrand.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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Derive the Simpson rule with f(x) = ax^2 + bx + c going through points xi−1, xi, and xi+1. Determine a, b, and c from the three equations given at the three data points first and then carry out the integration over the two slices with the quadratic curve being the integrand.

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