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anonymous
 one year ago
Let R be the region bounded by the curve y = ln (x), the xaxis and the line x = e. Find the area of R.
I need a quick answer with minimal work shown. Thanks
anonymous
 one year ago
Let R be the region bounded by the curve y = ln (x), the xaxis and the line x = e. Find the area of R. I need a quick answer with minimal work shown. Thanks

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SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.8dw:1435595958782:dw

Afrodiddle
 one year ago
Best ResponseYou've already chosen the best response.0Is there a graph you are suppose to give us?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's all the question says.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.8ok, so you have to integrate that from x=1 to x=e

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.8what I drew, is the picture, and x=1 is the limit of integration, because that is where the area above the xaxis starts, and x=e is the limit of integration because your region is bounded by x=e.

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.3the regeion is from x=1 to x=e

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.3so do integral of lnx from 1 to e

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.8\(\Large\color{slate}{\displaystyle\int\limits_{1}^{e}{\rm Ln}(x)~dx}\) like this.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So just set it up and solve it

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.8you know the integral of ln(x) right?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.8yup, that is right. Now you have to plug in the limits of integration.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.8\(\Large\color{slate}{\displaystyle\int\limits_{1}^{e}{\rm Ln}(x)~dx=\left(x{\rm Ln} {\tiny~}x~~x\right)~{\Huge}_{1}^{e}}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah I got that now thanks. How would I find the volume of the same problem on the x axis and also on the y axis?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.8Volume? Do you mean that the region we drew is rotated around some line?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah I got that now thanks. How would I find the volume of the same problem on the x axis and also on the y axis?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.8you mean the area, not the volume? if volume, then it is 3d, and probably this R is rotated around some line y=C or x=C. if area, then what area do you exactly what to find?
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