Discussion
Estimating that same \( \displaystyle\int_{0}^{2} x^{2}dx \) by Simpson's one-third rule with two strips gives
Answer: D
With the same ordinates and \( h = 1 \),
\[ I \;\approx\; \frac{1}{3}\left[0 + 4(1) + 4\right] \;=\; \frac{8}{3}. \]
Simpson's rule fits a parabola, and the integrand *is* a parabola, so the fit is exact. The rule is in fact exact for any cubic as well, which is why its error term involves the fourth derivative
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