1. ## volume problem

find the region by rotating about the y-axis

$y=e^{-x^2}~~~x-axis~~~~~x=0~~~~and ~~x=1$

I was thinking

$v=2pix\int_{0}^{1}e^{-x^2}$

2. but is that enough to bound the entire region or do I need another function?

3. You're on the right track, except that x belongs inside the integral.

$2{\pi}\int_{0}^{1}xe^{-x^{2}}dx$