Allied & ICAR Exam Bank • ALLIED_0099 NAT • 2 Marks

Section 1: Engineering Mathematics

Numerical Methods

Subtopic: Numerical integration – trapezoidal and Simpson's rule

Question Statement:

Evaluating $\int_0^2 x^3 dx$ using Simpson's $1/3^{\text{rd}}$ rule with $h = 1$ gives:

Answer Key:

4

Step-by-Step Solution & Explanation

$x_0=0, x_1=1, x_2=2$. $y_0=0, y_1=1, y_2=8$. $I = \frac{1}{3}[0 + 4(1) + 8] = 4.0$.
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