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

1. slaaibak

Here 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 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?

2. anonymous

ok does this look right? -e^(-x)(x+1) - (x^2/2e)

3. anonymous

and the area i got is 0.080301 does that sounds right? thanks for your help