# 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=x^2# and #y^2=x# rotated about the x-axis?

##### 1 Answer

To use shells, we take our representative slices parallel to the line we are revolving around. So the **thickness** will be **radius** will be

The height will be the greater

The limits of integration will be

The two curves are:

Solving the first equation for **function** of

The second equation already gives

Looking again at our sketch of the region, we see that the curve

The **height** is

The volume of the representative shell is:

And the limits of the region are

I am sure that you can finish from here.