Question
Find the area of the region bounded by the given curves.$ y = x^2 e^{-x} $ , $ y = xe^{-x} $
Step 1
We set $y = x^2 e^{-x}$ and $y = xe^{-x}$ equal to each other and solve for $x$: \[x^2 e^{-x} = xe^{-x}\] \[x^2 - x = 0\] \[x(x - 1) = 0\] So, $x = 0$ or $x = 1$ are the intersection points. Show more…
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