# How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region #y=2-x#, #2<=x<=4# rotated about the x-axis?

##### 1 Answer

Oct 9, 2015

Always graph the constraints first, then determine the correct integration formula.

#### Explanation:

Here is a graph of the constraints:

Now, without using calculus, you should visualize rotating this line around the x-axis will generate a **cone** with radius 2 and height 2. The volume of a cone is:

So, in advance of using calculus, we know the answer is

Now, using calculus and the **shell method** :

Because we rotate around the x-axis, integrate with respect to y:

hope that helped