What is the Volume of the Solid Using Cylindrical Shells for y=-e^(-x^2)?

sheldonrocks97
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Homework Statement



Find the volume of the solid using cylindrical shells:

y=e-x^2 y=0, x=0, x=1, about y-axis.

Homework Equations



How do I integrate xe^(-x^2)?

The Attempt at a Solution



2∏x∫0 to 1 xe^(-x^2) dx


2∏*-(e^(-1))/2)
 
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It's actually very easy think of a substitution.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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