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Extended Trapezoidal Rule
If we apply the Trapezoidal rule N -1 times and add the results, we get:
Big advantage is it builds on previous work:
- Coarsest step: average f at endpoints a and b.
- Next refinement: add value at midpoint to average.
- Next: add values at ¼ and ¾ points.
- And so on. This is implemented as trapzd() in NRiC.