GATE AG 2022 • Q19 NAT • 1 Mark

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Numerical integration – trapezoidal and Simpson's rule

Question Statement:

The power consumption readings (in watt) by an instrument at fixed intervals of time (in seconds) are tabulated below: Using Simpson's 1/3rd rule, the energy expenditure of the instrument in joule is __________. [round off to two decimal places]

Official Answer Key:

29.20 to 29.50

Step-by-Step Solution & Explanation

• n=6 intervals, h=0.6s. Formula: ∫f dx ≈ (h/3)[f₀+f₆+4(f₁+f₃+f₅)+2(f₂+f₄)] • 4(f₁+f₃+f₅)=4×24.2=96.8; 2(f₂+f₄)=2×15.0=30.0; f₀+f₆=19.8; total=146.6 • Energy = 0.2×146.6 = 29.32 J Computed value: 29.32 J (within official range 29.20–29.50) Section 2 — Farm Machinery

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