Find the area bounded by these two functions: $y = \frac{\ln x}{x}\quad\mbox{and}\quad y = \frac{1}{e} + \frac{(e^2+1)(x-e)}{e^2-1}.$
Find the area bounded by these two functions?
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calculus
integration
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0@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. – 2011-02-20
1 Answers
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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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0is the software available on Ubuntu? ADDED: okay, just searched it, it is not. Hope there is one. – 2011-02-20