GATE AG 2020 • Q46 NAT • 2 Marks

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Numerical integration – trapezoidal and Simpson's rule

Question Statement:

Using six intervals of $\pi/12$ each and Simpson's $1/3$ rule, evaluate $\int_{0}^{\pi/2} \sqrt{\cos\theta} \, d\theta$. (Rounded to 3 decimal places)

Official Answer Key:

1.186 to 1.189

Step-by-Step Solution & Explanation

With h=π/12 and ordinates y₀…y₆ = √(cos(0)), √(cos(π/12))…√(cos(π/2)): Simpson's 1/3 rule gives I = (h/3)[y₀+y₆+4(y₁+y₃+y₅)+2(y₂+y₄)] ≈ 1.187.

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