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GATE 2021 CE (CE1) – Question 37

Engineering Mathematics · Numerical Methods: Error analysis, algebraic equations, interpolation, differentiation, integration, ODEs · 2 marks · Multiple choice

Approximate $\int_0^1e^x dx$ using the trapezoidal rule with four equal subintervals.

  1. 1.718
  2. 1.727
  3. 2.192
  4. 2.718

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Correct answer: (B) 1.727

Explanation

With h=0.25, the composite rule gives $T=h[(1+e)/2+e^{0.25}+e^{0.5}+e^{0.75}]=1.7272219$. Rounded to three decimals, this is **1.727 (B)**. The exact integral e−1≈1.718 is not the requested approximation.