Evaluate ∫₀^1 xe^-x dx.

Definite Integrals & Area · Question 32 of 71

Question 32

HardOriginal question

Evaluate $\int_0^1 xe^{-x}\,dx$ .

1 - \frac{2}{e}

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e^{-1}

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1 - e^{-1}

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2 - \frac{2}{e}

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Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

By parts with $u = x$ , $dv = e^{-x}\,dx$ : $\int xe^{-x}\,dx = -xe^{-x} - e^{-x}$ .
$[-xe^{-x} - e^{-x}]_0^1 = \left(-\frac{2}{e}\right) - (-1) = 1 - \frac{2}{e}$ .

Worth noting

$1 - \frac{1}{e}$ is $\int_0^1 e^{-x}\,dx$ : the term $-xe^{-x}$ was dropped.

Ten questions from Definite Integrals & Area, at your own pace.

Ten questions from Definite Integrals & Area, at your own pace.