GATE 2019 BT – Question 60

Engineering Mathematics · Numerical Methods: Linear and nonlinear algebraic equations, trapezoidal and Simpson's rule, single step methods for ODEs · 2 marks · Numerical answer

Approximate $\int_{-1}^{1}f(x)dx$ by the trapezoidal rule, to 2 decimals. Values: x = −1,−2/3,−1/3,0,1/3,2/3,1; f(x) = 0.37,0.51,0.71,1.00,1.40,1.95,2.71.

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Correct answer: 2.20 to 2.50

Explanation

Spacing is h = 1/3. Composite trapezoidal integration gives $I\approx(h/2)[f_0+f_6+2(f_1+\cdots+f_5)]$. The endpoint sum is 3.08 and interior sum 5.57, so $I\approx(3.08+2(5.57))/6=2.37$.

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