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I think I'm over thinking this because I'm coming up blank. Any help would be appreciated. Here is the question:

Derive the Simpon's Rule for numerical integration in a interval $[x_{0}, x_{2}]$ $$\int_{x_{0}}^{x_{2}} f(x) dx = \frac{h}{3}(f_{0}+4f_{1}+f_{2}),$$ where $x_{i}=x_{0}+ih, f_{i}=f(x_{i}).$

primer
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1 Answers1

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Hint: With 3 data points, one can interpolate a quadratic polynomial. Verify that Simpon's rule is exact for quadratic polynomials.

lhf
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