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GATE 2026 BT – Question 51

Engineering Mathematics · Numerical Methods: Linear and nonlinear algebraic equations, trapezoidal and Simpson's rule, single step methods for ODEs · 2 marks · Numerical answer

Consider the equation $\frac{dy}{dx} = \frac{1}{x}$

The value of the integral $\int_1^2 dy$ using trapezoidal method and interval $h = 0.25$ is ________. (rounded off to two decimal places)

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Correct answer: 0.69 to 0.71

Explanation

$\int dy = \int_1^2\frac{dx}{x}$. The values of $\frac{1}{x}$ at $x = 1, 1.25, 1.5, 1.75, 2$ are $1, 0.8, 0.6667, 0.5714, 0.5$. The trapezoidal rule gives $\frac{0.25}{2}[1 + 2(0.8 + 0.6667 + 0.5714) + 0.5] = 0.125 \times 5.576 = 0.70$.