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The integral ∫₁³ (1/x) dx, when evaluated by using Simpson’s 1/3 rule on two equal subintervals each of length 1, equals

1. 1.000
2. 1.098
3. 1.111
4. 1.120

Correct answer: 1.111

Solution

Using h=1 and nodes x=1,2,3 with f=1, 0.5, 0.3333: Simpson 1/3 = (1/3)[1 + 4(0.5) + 0.3333] = (1/3)(3.3333) = 1.111. (The exact ln3=1.0986 corresponds to the stored 1.098, but Simpson's rule yields 1.111.)

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