Discussion
Estimating \( \displaystyle\int_{0}^{2} x^{2}dx \) by the trapezoidal rule with two strips gives
Answer: A
With \( h = 1 \) the ordinates are \( y_{0} = 0 \), \( y_{1} = 1 \), \( y_{2} = 4 \), so
\[ I \;\approx\; \frac{1}{2}\left[0 + 4 + 2(1)\right] \;=\; 3. \]
The exact value is \( 8/3 \approx 2.667 \), so the rule overestimates by a third. It always does for a convex integrand, the chords lying above the curve
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