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GATE 2016 ME (ME2) – Question 15

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

Numerical integration using trapezoidal rule gives the best result for a single variable function, which is

  1. linear
  2. parabolic
  3. logarithmic
  4. hyperbolic

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Show answer and explanation

Correct answer: (A) linear

Explanation

The trapezoidal rule replaces a function on each interval by a straight line joining its endpoint values. This replacement is exact for a linear function, so its integral has zero quadrature error. Thus **linear, A**. Curved functions generally have a nonzero second-derivative error term.