Fins the volume if the solidobtained by rotating the region bounded by y=x^(1/3) and y=x/4
Here is a happy little animated diagram showing the region rotated about the x-axis. Enjoy.
And yes, that is what I gave you. Both methods rotating about the x-axis. Shells and washers.
When we use shells, the cross sections are parallel to the axis about which we are revolving. Since they are parallel to the x-axis, we can picture them being stacked up the y-axis. That is why we integate w.r.t y in that case. We solve the equations for x in terms of y and change the limits to the y limits, which are 0 to 2.