GATE 2024 AE – Question 31

Engineering Mathematics · Numerical Methods: Bisection and Newton-Raphson, numerical differentiation, trapezoidal and Simpson's rules · 1 mark · Numerical answer

Using Trapezoidal rule with one interval, the approximate value of the definite integral: $\int_1^2 \frac{dx}{1 + x^2} = $ ______ (rounded off to 2 decimal places).

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Correct answer: 0.34 to 0.36

Explanation

With one interval, $\int_a^b f\,dx \approx \frac{b - a}{2}[f(a) + f(b)] = \frac{1}{2}\left[\frac{1}{2} + \frac{1}{5}\right] = 0.35$.