• anonymous
Calculus: sketch and then calculate the area bounded by the graphs y=xe^-x and y=(1/e)x
  • Stacey Warren - Expert
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  • schrodinger
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  • slaaibak
Here is the sketch:^-x%3B+f%28x%29%3D%281%2Fe%29x Now, you must calculate the area. On the graph, we can see the x-bounds, but if you want to calculate, you must set the two graphs equal to each other to find the x-intercepts. \[{x \over e} = xe^{-x} \] 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
ok does this look right? -e^(-x)(x+1) - (x^2/2e)
  • anonymous
and the area i got is 0.080301 does that sounds right? thanks for your help

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