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GATE 2024 MN – Question 40

Engineering Mathematics · Numerical Methods · 2 marks · Multiple choice

For $I=\int_1^3(x^3+6)dx$, find the magnitude of Simpson one-third-rule error using step 1.

  1. 0
  2. 1.0
  3. 1.5
  4. 2.0

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Correct answer: (A) 0

Explanation

Simpson’s one-third rule integrates every cubic polynomial exactly. Directly, the values are 7, 14, 33, so the result is(7+4×14+33)/3=32. The exact integral is[x⁴/4+6x]₁³=32. Hence error 0, A.

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