GATE 2026 MT – Question 45
Taking the number of intervals as $n=3$, the value of $\displaystyle\int_0^{0.3}e^{-x^2}\,dx$ using the trapezoidal method is ________. (Rounded off to two decimal places.)
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Correct answer: 0.27 to 0.31
Explanation
The step size is $h=(0.3-0)/3=0.1$. At $x=0,0.1,0.2,0.3$, the function values are approximately $1,0.9900498,0.9607894,0.9139312$.
The composite trapezoidal rule gives $I\approx0.1[(1+0.9139312)/2+0.9900498+0.9607894]=0.2907805$. Rounded to two decimals, enter **0.29**.