The question is : Find the volume of the solid obtained by rotating about the $y$-axis the region bounded by the curves $y= e^{-2x^2}$, $y=0$, $x=0$, $x=1$.
Should the bounds for the problem be taken from the $y$-axis or the $x$-axis?
I think that the integral for this problem would be:
$$\prod\int(e^{-2x^2})^2\,dx,$$
or do i have to rewrite the equation in terms of x?
For a solid of revolution about the $y$ axis, the integral looks like
$$\pi \int_{e^{-2}}^1 dy \: (x(y))^2 = \frac{\pi}{2} \int_{e^{-2}}^1 dy \: (-\log{y})$$