How to calculate this integral?
$$\int_{\frac{1}{e}}^{e}|\ln x| dx$$
It is an obvious integral if the function is under the integral without modulus. The whole catch is in the module.
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7$\begingroup$ Where is ln(x) positive and negative? $\endgroup$– EnlightenedFunkyMar 25, 2021 at 18:14
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$\begingroup$ desmos.com/calculator/ajhisuekar $\endgroup$– EnlightenedFunkyMar 25, 2021 at 18:18
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1 Answer
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You can use that
$$ \int_{1/e}^{e}\left|\ln\left(x\right)\right|\text{d}x=\int_{1/e}^{1}\left|\ln\left(x\right)\right|\text{d}x+\int_{1}^{e}\left|\ln\left(x\right)\right|\text{d}x $$ Can you now discuss the value of $\left|\ln\left(x\right)\right|$ in each interval ?
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$\begingroup$ I think the upper limit of the second integral should be $e$, not $1/e$, right? $\endgroup$– an4sMar 26, 2021 at 4:26
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