I wanted to ask what I think is a fairly simple question for most of you on here!
Revolve the curve $$y=e^{-x}$$ bounded by $y=0$, $x=0$, $x=-1$ about the $x=1$ axis. I am supposed to use the method of shells. Here is my attempt at a solution: $$2\pi\int_{-1}^0 (1+x)(e^{-x})dx$$ Which comes out to $2\pi(e-2)$. However the correct answer is $2\pi(e)$. Any help would be great as my final is coming up.
Radius of cylinder is 1-x. The fact that x is negative is not relevant.