First slide

Evaluation of definite integrals

Question

$\int_{0}^{1} (x - 1) e^{- x} d x =$

Easy

A

$- \frac{1}{e}$
B

$\frac{1}{e}$
C

e
D

2e

Solution

$\int_{0}^{1} (x - 1) e^{- x} d x$
$= {[\frac{(x - 1) e^{- x}}{- 1}]}_{0}^{1} - \int_{0}^{1} \frac{e^{- x}}{- 1} d x$

$= - (0 + 1) - {(\frac{e^{- x}}{+ 1})}_{0}^{1}$

$= - 1 - e^{- 1} + 1 = \frac{- 1}{e}$

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