Allied & ICAR Exam Bank • ALLIED_2770 NAT • 2 Marks

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Numerical integration – trapezoidal and Simpson's rule

Question Statement:

Using the Trapezoidal rule with step size $h = 1$ to integrate $f(x)$ over $[0, 3]$ with values $f(0) = 1, f(1) = 3, f(2) = 4, f(3) = 2$ gives:

Answer Key:

8.5

Step-by-Step Solution & Explanation

$I = \frac{h}{2} [f(0) + 2(f(1) + f(2)) + f(3)] = \frac{1}{2} [1 + 2(3 + 4) + 2] = \frac{1}{2} [1 + 14 + 2] = \frac{17}{2} = 8.5$.
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