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GATE 2022 PI – Question 12

Engineering Mathematics · Numerical Methods · 1 mark · Multiple choice

Numerically integrate y = 2x+5 from x = 1 to 3 using ordinates at x = 1,2,3. Which statement is true?

  1. Simpson’s 1/3 rule is exact, but trapezoidal is not.
  2. Trapezoidal is exact, but Simpson’s 1/3 rule is not.
  3. Both Simpson’s 1/3 and trapezoidal rules are exact.
  4. Neither rule is exact.

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Correct answer: (C) Both Simpson’s 1/3 and trapezoidal rules are exact.

Explanation

The integrand is linear, so trapezoidal integration is exact; Simpson’s rule is exact for polynomials up to degree three. Ordinates are 7,9,11. Trapezoidal gives (7+2×9+11)/2 = 18; Simpson gives (7+4×9+11)/3 = 18, agreeing with the integral. **C**.

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