Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

share|improve this question
    
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

1 Answer 1

enter image description here

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.

share|improve this answer
    
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

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.