Question Bank • QB_SUB_EM_0181 NAT • 2 Marks

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Numerical integration – trapezoidal and Simpson's rule

Question Statement:

Using the Trapezoidal rule with a single interval ($h = 1$), evaluate $\int_0^1 x^2\, dx$:

Answer Key:

0.5

Step-by-Step Solution & Explanation

Trapezoidal rule for 1 interval: $\int_0^1 f(x)\, dx \approx \frac{h}{2} [f(0) + f(1)] = \frac{1}{2} [0^2 + 1^2] = 0.50$ (Exact integral is $1/3 \approx 0.333$).
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