Math Help - Volumes Using Shell Method Question

1. Volumes Using Shell Method Question

Ok so I am a bit confused by the shell method. My prof has given us a general forumula for using the shell method which I understand $V=\int^b_a 2\pi (x-M)[u(x)-l(x)]dx$
where $M$ is the line which to rotate around, $u(x)$ is the upper curve, and $l(x)$ is the lower curve.

When presented with the following question where we have to rotate about $x=5$ as shown on the following graph when I simply substituted 5 in for M, giving me $(x-5)$ for the first part I get the wrong answer but $(5-x)$ gives me the correct the answer.

Looking at some of the examples I have it would appear that if the axis of rotation is to the right of our functions it reverses the order of $(x-M)$ to $(M-x)$. Is this correct to assume?

2. Originally Posted by jfinkbei
Looking at some of the examples I have it would appear that if the axis of rotation is to the right of our functions it reverses the order of $(x-M)$ to $(M-x)$. Is this correct to assume?
Yes, the (x-M) or (M-x) is the radius of your shell, which you want to always be a positive number.

Volume of a shell = $2\pi(radius)(altitude)(thickness)$

Where the radius is the the positive distance between the curve and axis of rotation, the altitude is your function (or difference if there are two functions) and thickness is dx.