GATE 2024 MT – Question 52
The integral $\int_0^1xe^{-x}\,dx$ is ______ (two decimal places).
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Correct answer: 0.24 to 0.28
Explanation
Integration by parts with $u=x$ and $dv=e^{-x}dx$ gives the antiderivative $-(x+1)e^{-x}$.
At the limits, $[-(x+1)e^{-x}]_0^1=1-2/e=0.26424\ldots$.
The answer is **0.26**.