Cylindrical shell radius when rotating about x=2

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Xetman
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Homework Statement


Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the curves about the specified axis.

y=x^4, y=0, x=1; about x=2

2. The attempt at a solution

I know how to do the problem, except how to find the radius. Like I know if it was about the x-axis then the radius would just be x. But since it's about x=2, would the radius be 2-x? If it is 2-x, why?

I'm guessing it's 2-x because there was a similar problem earlier in the book that showed this being the radius when it was about x=2.
 

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Hi Xetman! :smile:

(try using the X2 button just above the Reply box :wink:)
Xetman said:
II know how to do the problem, except how to find the radius. Like I know if it was about the x-axis then the radius would just be x. But since it's about x=2, would the radius be 2-x? If it is 2-x, why?

The region is a sort of collar centred around x = 2.

So your cylindrical shells will also be centred around x = 2 …

so the radius of the shell that goes through (x,0,0) is the distance of (x,0,0) from (2,0,0). :wink: