GATE 2013 CS (CS1) – Question 33
At x=0,0.3,0.6,0.9,1.2,1.5,1.8,2.1,2.4,2.7,3.0 the values of f are 0,0.09,0.36,0.81,1.44,2.25,3.24,4.41,5.76,7.29,9.00. Approximate its integral from zero to three by the trapezoidal rule.
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Correct answer: (D) 9.045
Explanation
The spacing is h=0.3. Interior values sum to 25.65; half the endpoint sum is 4.5. The trapezoidal approximation is $0.3(25.65+4.5)=9.045$, D. The tabulated values happen to equal x², but the requested rule gives a different result from its exact integral nine.