# 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=6x^2#, #y=6sqrtx# rotated about the y-axis?

##### 1 Answer

The normal revolution method calls for:

where one stacks circle analogs of varying radius

In contrast, the shell method calls for a volume formula as such:

where the way

Let's see how this looks.

graph{6x^2 [-2, 2, -1, 1]}

graph{6sqrtx [-2, 2, -2, 6]}

If you layer these graphs on top of each other, you can see that they intersect to form a "stretched lemon" of sorts. Let's find where they intersect to determine our

Besides

Thus, the practical interval is

So, taking the area between the two curves as the difference between the top