Multiple choice

The estimate of $\int\limits_{0.5}^{1.5} \frac{dx}{x}$ obtained using Simpson’s rule with three point function evaluation exceeds the exact value by

  1. 0.235

  2. 0.068

  3. 0.024

  4. 0.012
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Simpson's rule for 1/x from 0.5 to 1.5 with three points (h=0.5): x=0.5, 1.0, 1.5. Integral = (h/3) * (f(0.5) + 4f(1.0) + f(1.5)) = (0.5/3) * (2 + 4 + 0.666) = 0.1666 * 6.666 = 1.111. Exact value = ln(1.5) - ln(0.5) = ln(3) = 1.0986. Difference = 1.111 - 1.0986 = 0.0124.

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