GATE 2019 ME (ME1) – Question 28

Engineering Mathematics · Numerical Methods: Algebraic equations, integration by trapezoidal and Simpson rules, ODE methods · 1 mark · Numerical answer

Estimate $\int_2^4x^3\,dx$ using the trapezoidal rule with two equal segments.

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Correct answer: 63 to 63

Explanation

The step is h=(4-2)/2=1 and the ordinates are8,27,64. The composite trapezoidal estimate is $h[f(2)+2f(3)+f(4)]/2=(8+54+64)/2=\mathbf{63}$. This is the requested numerical estimate rather than the exact integral60.