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GATE 2021 ME (ME2) – Question 28

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

Value of $\int_4^{5.2}\ln x\,dx$ using Simpson’s one-third rule with interval size 0.3 is

  1. 1.83
  2. 1.60
  3. 1.51
  4. 1.06

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Correct answer: (A) 1.83

Explanation

There are four intervals with nodes 4,4.3,4.6,4.9,5.2. Simpson’s rule gives $I=(0.3/3)[\ln4+4\ln4.3+2\ln4.6+4\ln4.9+\ln5.2]$.

The result is approximately 1.8278, hence **1.83 (A)**. Alternating 4,2,4 weights are essential.