GATE AG 2008 • Q4 MCQ • 1 Mark

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Numerical integration – trapezoidal and Simpson's rule

Question Statement:

A function f(x) is evaluated as 1, 1.5, 2.2 and 3.4 at four values of x having intervals of 0.5. The area under the curve f(x) using trapezoidal rule is

Options:

  • (A) 1.95
  • (B) 2.45
  • (C) 2.95
  • (D) 3.45

Official Answer Key:

C

Step-by-Step Solution & Explanation

Trapezoidal rule: A = h[(y₀+y₃)/2 + y₁+y₂] = 0.5×[(1+3.4)/2 + 1.5+2.2] = 0.5×[2.2+3.7] = 0.5×5.9 = 2.95.

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