# 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 = 1 + x^2#, #y = 0#, #x = 0#, #x = 2# rotated about the line #x=4#?

##### 1 Answer

#### Explanation:

This is a graph of the region that will be revolved around the vertical line

graph{(y-1-x^2)(y)( sqrt(2-x) )(sqrt(x)) / (sqrt(2-x))/(sqrt(x))<=0 [0, 6, -1.51, 6.39]}

Recall the general form of the volume of a solid of revolution using the shells method when you are revolving about a vertical line:

The hardest conceptual part here is the radius. Since the axis of revolution is

(Why? Draw a segment from

Thus: