Allied & ICAR Exam Bank • ALLIED_2771 MSQ • 2 Marks

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Numerical integration – trapezoidal and Simpson's rule

Question Statement:

Which of the following statements regarding Newton–Cotes integration formulas are TRUE?

Options:

  • (A) Trapezoidal rule integrates linear polynomials ($ax + b$) exactly
  • (B) Simpson's 1/3 rule integrates cubic polynomials exactly
  • (C) Simpson's 1/3 rule requires an even number of intervals
  • (D) Simpson's 3/8 rule requires an odd number of intervals

Answer Key:

A, B, C

Step-by-Step Solution & Explanation

(A), (B), (C) are standard mathematical facts. (D) is false because 3/8 rule requires $n$ to be a multiple of 3, which can be even or odd.
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