The region bounded by $\displaystyle y=e^{-x^2},\ y=0,\ x=0,$ and $\displaystyle x=1$ is revolved about the y-axis. Find the volume of the resulting solid.

I know that the answer is $\displaystyle 2\pi\int_0^1xe^{-x^2}$, however I am not sure how to get there. I drew a picture, and I can't tell if I'm supposed to approximate with disks or shells...or approach it a different way. Any insight offered is appreciated. Thanks in advance.