tony873004

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Use the method of cylindrical shells to find the volume generated by rotating the region bounded by y=e^(-x^2), x=0, x=1, rotated about the y axis.

[tex]

\begin{array}{l}

\int\limits_{\rm{0}}^{\rm{1}} {\pi r^2 h\,\,dx} = \int\limits_{\rm{0}}^{\rm{1}} {\pi x^2 e^{ - x^2 } \,\,dx} = \\

\\

\pi \int\limits_{\rm{0}}^{\rm{1}} {x^2 e^{ - x^2 } \,\,dx} \\

\end{array}

[/tex]

I just don't know how to anti-deriv xe^(-x^2). I've tried substitution with u= -x2 with no joy. I'll bet this is easy, but it's got me stumped.

**1. Homework Statement**

**2. Homework Equations**

**3. The Attempt at a Solution**