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Function f is known at the following points: x: 0, 0.3, 0.6, 0.9, 1.2, 1.5, 1.8, 2.1, 2.4, 2.7, 3.0 f(x): 0, 0.36, 0.81, 1.44, 2.25, 3.24, 4.41, 5.76, 7.29, 9.00 The value of ∫₀³ f(x) dx computed using the trapezoidal rule is

1. 8.983
2. 9.003
3. 9.017
4. 9.045

Correct answer: 9.045

Solution

With h=0.3 and f(x)=x^2 on [0,3], the trapezoidal rule gives 0.3*(0/2 + sum of interior + 9/2) = 9.045. The trapezoidal rule overestimates a convex function, so the result is just above the exact value 9.

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