Volume of revolution at line x=-4

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To find the volume of the solid formed by rotating the region bounded by y=0, y=sin(6x), x=0, and x=6 around the line x=-4, the cylindrical method is applicable. The integral setup involves determining the correct expression for the radius, which is influenced by the distance from the axis of rotation. The correct formulation for the volume integral is 2*pi*(4+x)dx*sin(6x), as it accounts for the distance from the line x=-4. After initial confusion, the correct approach was clarified, leading to a solution. The discussion emphasizes understanding the cylindrical method for volume calculations around a non-standard axis.
~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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