How do you use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by #y^2=4x#, x=y revolved about the y-axis?
Draw a picture (sketch) of the region.
Note that the graphs intersect where
And that happens at
We are asked to use shells, so we take thin representative rectangles parallel to the axis of rotation. In this case that is the
The slice has solid black boundaries and the radius to the axis of rotation is shown as a dashed black line.
Since the thin part is
The lower function is
The volume of a representative shell is
In this case, we have
(details left to the student)
# = (128pi)/15#