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GATE 2026 PI – Question 15

Engineering Mathematics · Numerical Methods · 1 mark · Multiple choice

Using numerical integration, which option most closely approximates $\int_0^1e^{-x^2}dx$?

  1. $1$
  2. $1/e$
  3. $(e+1)/(2e)$
  4. $(1+e)/2$

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Correct answer: (C) $(e+1)/(2e)$

Explanation

The one-panel trapezoidal rule gives $I\approx(1-0)[f(0)+f(1)]/2=(1+e^{-1})/2=(e+1)/(2e)\approx0.68394$. The actual integral is about 0.74682, so among the listed values this is also the closest. **C**.

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