# How do you use the method of cylindrical shells to find the volume generated by rotating the region bounded by y=e^(−x^2), y=0, x=0, and x=1 about the y axis?

Oct 12, 2015

Draw a sketch, then integrate using the shell method with respect to x.

#### Explanation:

Here is sketch of the problem:

Using the formula for the Shell Method:

$2 \pi {\int}_{0}^{1} \left(x\right) \left({e}^{- {x}^{2}} - 0\right) \mathrm{dx}$

You can use substitution {$u = {x}^{2}$} to solve.

$= \pi \left(1 - {e}^{-} 1\right)$

Answer $\approx 1.986$

Hope that helps