# Find the area bounded by these two functions?

Find the area bounded by these two functions: $$y = \frac{\ln x}{x}\quad\mbox{and}\quad y = \frac{1}{e} + \frac{(e^2+1)(x-e)}{e^2-1}.$$

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Could you kindly typeset the question? –  user17762 Feb 20 '11 at 0:59
And please ask questions, don't give orders. –  Arturo Magidin Feb 20 '11 at 1:17
@Arturo: I think you were also editing when I typeset it. I have undone my edit. Yours look much better, –  user17762 Feb 20 '11 at 1:18
@Sivaram: If you don't mind, I'll rollback. Displays are better with the fractions, I want to keep the second function as it was typed, and the quotebox at least makes it seem like the OP is quoting, not ordering the group around. –  Arturo Magidin Feb 20 '11 at 1:19

The area is the integral $\displaystyle \int_{x_1}^{x_2} y dx$ where $y=y_{\text{upper}}-y_{\text{lower}}$.

$y_{\text{upper}} = \frac{\ln(x)}{x}$ and $y_{\text{lower}} = \frac{1}{e} + \frac{e^2+1}{e^2-1}(x-e)$.

$(x_1,y_1)$ and $(x_2,y_2)$ are obtained by equating $y_{\text{lower}}$, $y_{\text{upper}}$

Note: It is easy to obtain $(x_1,y_1)$ and $(x_2,y_2)$ by guessing.

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I was wondering how you made the plot? Thanks! –  Tim Feb 20 '11 at 1:26
@Tim: I use the grapher software on os x to make such plots. –  user17762 Feb 20 '11 at 1:28
is the software available on Ubuntu? ADDED: okay, just searched it, it is not. Hope there is one. –  Tim Feb 20 '11 at 1:33