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GATE 2020 ME (ME1) – Question 36

Engineering Mathematics · Numerical Methods: Algebraic equations, integration by trapezoidal and Simpson rules, ODE methods · 2 marks · Multiple choice

Evaluate $\int_{-1}^{1.4}x|x|\,dx$ using Simpson’s 1/3 rule with step size h = 0.6.

  1. 0.914
  2. 1.248
  3. 0.581
  4. 0.592

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Correct answer: (D) 0.592

Explanation

The five nodes are −1,−0.4,0.2,0.8,1.4 and f-values −1,−0.16,0.04,0.64,1.96. Simpson’s sum is $(0.6/3)[-1+1.96+4(-0.16+0.64)+2(0.04)]=0.592$. Therefore **D**, rather than using the exact integral across the cusp.