Volume of revolution at line x=-4

~Sam~
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Homework Statement



Find the volume of the solid obtained by rotating the region bounded by the curves y=0,y=sin(6x),x=6,x=0 about the axis x=−4.


Homework Equations



cylindrical method? circumference*thickness*height


The Attempt at a Solution



So I'm not sure how to write the integral when it rotates along the line x=-4 ..would it be like 2*pi*(-4+x)dx*sin(6x)? or 2*pi*(4-x)dx*sin(6x)? Or something completely different?
 
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Nevermind..I got it!
 
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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