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I'm using a quadrature to estimate the integral of a function.

Intuitively, I know that if the function is a very smooth function, the quadrature will perform well at a low order (few samples).

If however, the function in more complex, I'll need to sample it more frequently for the quadrature to be as accurate.

I'm wondering if there's some equation that expresses this intuition. Something that I can point to and use to explain why more complex functions require a higher order quadrature for the same level of accuracy.

I think the expression should contain some reference to the function's derivative.

Thanks.

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# Estimating Error in a Quadrature

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