The GATE Grind

GATE 2024 BT – Question 65

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

The absolute relative error in evaluating the integral $\int_0^1 x^2dx$ by the trapezoidal rule with the step size 0.25 is ________ % (rounded off to 2 decimal places).

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 3.11 to 3.15

Explanation

With $h = 0.25$: $T = 0.25\left[\frac{0 + 1}{2} + 0.0625 + 0.25 + 0.5625\right] = 0.34375$. The exact value is $\frac13$, so the relative error is $\frac{0.34375 - 0.33333}{0.33333} = 3.125\% \approx 3.13\%$.