GATE AG 2010 • Q13 MCQ • 1 Mark

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Numerical integration – trapezoidal and Simpson's rule

Question Statement:

The error in using trapezoidal rule for finding the value of $\int_{0}^{1} \frac{dx}{1+x}$ is:

Options:

  • (A) 0.0368
  • (B) 0.0468
  • (C) 0.0568
  • (D) 0.0668

Official Answer Key:

C

Step-by-Step Solution & Explanation

Exact value: ∫₀¹dx/(1+x) = ln 2 = 0.693147. Single-interval trapezoidal estimate: (1/2)[f(0)+f(1)] × 1 = (1/2)(1 + 0.5) = 0.75. Error = 0.75 − 0.693147 = 0.0569 ≈ 0.0568, matching (C).

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