Question Bank • QB_EM_164
NAT • 2 Marks
Section 1: Engineering Mathematics
Numerical Methods
Subtopic: Numerical integration – trapezoidal and Simpson's rule
Question Statement:
Evaluate the integral $I = \int_0^2 x^2\, dx$ numerically using the Trapezoidal Rule with 2 equal sub-intervals ($h = 1.0$).
Step-by-Step Solution & Explanation
Step size $h = 1.0$. Grid points: $x_0 = 0, x_1 = 1, x_2 = 2$.
Function values:
$y_0 = 0^2 = 0$
$y_1 = 1^2 = 1$
$y_2 = 2^2 = 4$
Trapezoidal rule:
$I = \frac{h}{2} [y_0 + 2y_1 + y_2] = \frac{1.0}{2} [0 + 2(1) + 4] = \frac{1}{2} [6] = 3.0$
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