Mathematics

# Integrate: $\displaystyle \int _{ 1/e }^{ e }{ \left| x \right| } dx=$

0

##### SOLUTION

Consider the given integral.

$I=\int_{e}^{1/e}{\dfrac{\ln x}{x}}dx$

Let $t=\ln x$

$dt=\ln xdx$

Therefore,

$I=\int_{1}^{-1}{tdt}$

$I=\left[ \dfrac{{{t}^{2}}}{2} \right]_{1}^{-1}$

$I=\left[ \dfrac{{{\left( -1 \right)}^{2}}}{2}-\dfrac{{{1}^{2}}}{2} \right]$

$I=0$

Hence, this is the answer.

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One Word Medium Published on 17th 09, 2020
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