Confused about cylindrical shell radius?

For the region bounded by y=x^4, y=0 and x=1; rotated about x=2, the radius of a typical shell is 2-x.

But, for the region bounded by y=4x-x^2 and y=3; rotated about x=1, the radius of a typical shell is x-1.

Can anyone explain why the radius is x-1, instead of 1-x? Or what's the thought process behind figuring out what the radius of a shell is?

1 Answer
Mar 9, 2018

In the second case, #x# is to the right of #1#, so the distance is #x-1#

Explanation:

Sketch the graphs.

In the first problem #x# is to the left of the axis of rotation, so the distance, which is #x_"greater" - x_"lesser"# will be #2-x#

In the second problem the axis of rotation is to the left of #x#, so the distance, which is #x_"greater" - x_"lesser"# will be #x-1#