Allied & ICAR Exam Bank • ALLIED_0802 NAT • 2 Marks

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Numerical integration – trapezoidal and Simpson's rule

Question Statement:

Evaluating $\int_0^4 (2x + 1) dx$ using the trapezoidal rule with a single interval ($h = 4$) gives $I = \frac{4}{2}[f(0) + f(4)]$. Since $f(0) = 1$ and $f(4) = 9$, the value of $I$ is:

Answer Key:

20

Step-by-Step Solution & Explanation

$I = 2 \times (1 + 9) = 2 \times 10 = 20.0$. Analytical value is $[x^2 + x]_0^4 = 16 + 4 = 20$.
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