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anonymous
 4 years ago
Calculus: sketch and then calculate the area bounded by the graphs y=xe^x and y=(1/e)x
anonymous
 4 years ago
Calculus: sketch and then calculate the area bounded by the graphs y=xe^x and y=(1/e)x

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slaaibak
 4 years ago
Best ResponseYou've already chosen the best response.1Here is the sketch: http://www.wolframalpha.com/input/?i=g%28x%29%3Dxe^x%3B+f%28x%29%3D%281%2Fe%29x Now, you must calculate the area. On the graph, we can see the xbounds, but if you want to calculate, you must set the two graphs equal to each other to find the xintercepts. \[{x \over e} = xe^{x} \] we can clearly see x=zero would solve this, as well as x=1. from the graph we can see xe^x is bigger, so our integral becomes: \[\int\limits_{0}^{1} (xe^{x}  {x \over e}) dx \] \[\int\limits_{0}^{1} xe^{x} dx  \int\limits_{0}^{1} {x \over e} dx\] Can you take it from there?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok does this look right? e^(x)(x+1)  (x^2/2e)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0and the area i got is 0.080301 does that sounds right? thanks for your help
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