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GATE 2026 ME – Question 15

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

The exact solution of $\int_0^4 \dfrac{dx}{1 + x}$ is represented as $n$.

If $m$ represents numerically evaluated value of the above integral using Trapezoidal rule by considering four equal subintervals in the range of $x$, then $(m - n)$ is

  1. 0.074
  2. $-0.074$
  3. $-0.003$
  4. 0.003

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Show answer and explanation

Correct answer: (A) 0.074

Explanation

The exact value is $n = \ln 5 = 1.6094$. With four equal subintervals, $h = 1$ and the function values are 1, 0.5, 0.3333, 0.25 and 0.2. The trapezoidal rule gives $m = \frac{1}{2}(1 + 0.2) + 0.5 + 0.3333 + 0.25 = 1.6833$. So $m - n = 0.074$.