GATE 2026 CH – Question 35

Engineering Mathematics · Numerical Methods: Algebraic equations, integration, ODEs and finite-difference methods · 1 mark · Numerical answer

Using single step trapezoidal rule, the value of $\int_0^{0.5} (1 + 16x - 20x^2)\,dx$ is ______ (rounded off to two decimal places).

Show answer and explanation

Correct answer: 1.24 to 1.26

Explanation

The function is $f(0) = 1$ and $f(0.5) = 1 + 8 - 5 = 4$. A single trapezoid gives $\frac{0.5 - 0}{2}(1 + 4) = 1.25$.