How do I show that$$\int_a^bf(x)dx - I_1 = - \frac{h^5}{90}f^{(4)} (\xi)$$with $\xi \in [a,b]$ and$$I_1 := \frac{h}{3}(f(a) + 4f\left( \frac{a+b}{2}\right) + f(b))$$and $h= \frac{b-a}{2}$. I was thinking about about the mean value theorem somewhere, but I am not sure how to apply it to get to the result.
$\endgroup$ 2 Reset to defaultError of Simpson's Rule
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